Banach Space - Science topic

This study aims to examine the SIA ICR model with chronic infection therapy and data analysis worldwide and its actual implications. The boundedness and uniqueness solution of such an HBV model are confirmed, and Banach space is used to look for bounded discoveries. The developed system’s uniqueness is investigated to verify if it has a unique solu...

This book is devoted on some recent investigations of some classes partial differential equations in Sobolev and analytic spaces. The book contains twelve chapters. Chapter 1 is entirely devoted to the presentation of definitions and results necessary as a result of this work. We first recall a few basic results on the linear, metric, normed and Ba...

In this paper, we study a class of bi-nonlocal fourth-order discrete problems involving p(k)-Laplacian operator in a finite-dimensional Banach space. Using the variational method and the (S+) mapping theory, we investigate the existence and multiplicity of nontrivial solutions, subject to the condition that the parameters are sufficiently large.

We consider generalized gradient systems in Banach spaces whose evolutions are generated by the interplay between an energy functional and a dissipation potential. We focus on the case in which the dual dissipation potential is given by a sum of two functionals and show that solutions of the associated gradient-flow evolution equation with combined...

In this paper, we analyze various classes of multi-dimensional ρ- almost periodic type functions F : I × X → Y and multi-dimensional (ω, ρ)- almost periodic type functions F : I×X → Y, where n ∈ N, ∅ ≠ I ⊆ R^n, X and Y are complex Banach spaces and ρ is a binary relation on Y. The proposed notion is new even in the one-dimensional setting, for the...

For each n-dimensional real Banach space X, each positive integer m, and each bounded set A⊆X with diameter greater than 0, let βX(A,m) be the infimum of δ∈(0,1] such that A⊆X can be represented as the union of m subsets of A, whose diameters are not greater than δ times the diameter of A. Estimating βX(A,m) is an important part of Chuanming Zong’s...

This paper presents a systematic approach for analyzing optimal feedback control systems governed by Hilfer fractional neutral evolution equations with history-dependent operators in separable reflexive Banach spaces. We initially investigate the existence of mild solutions for the system using the Darbo-Sadovskii fixed point theorem. Subsequently,...

It has been known that the fractional ODEs involving Riemann-Liouville fractional derivatives maintain many "analogies" of the classic elliptic-type properties, including maximum principles, Hopf's Lemma, the existence of real eigenvalues, etc. However, in this short work, we construct a counterexample demonstrating that Caputo-type fractional oper...

We present an abstract maximal $L^p$-regularity result up to $T = \infty$ on a Banach space, that is tuned to capture (linear) PDEs of parabolic type, defined on a bounded domain and subject to finite dimensional, boundary controls and boundary sensors, in feedback form. It improves Lasiecka et al. (2021), which covered boundary controls and interi...

In this paper, inspired by the previous work in [Ngai, Tron, Vu, Thera, Set-Val. Var. Anal. 28 (2020), 61-87], we continue to study a general regularity model called directional metric pseudoregularity of set-valued mappings defined on Banach spaces, which is stronger than the one given in the reference above. The characterizations of this model th...

Vesel\'y (1997) studied Banach spaces that admit $f$-centers for finite subsets of the space. In this work, we introduce the concept of $\mr{F}$-simultaneous approximative $\tau$-compactness property ($\tau$-$\mr{F}$-SACP in short) for triplets $(X, V,\mf{F})$, where $X$ is a Banach space, $V$ is a $\tau$-closed subset of $X$, $\mf{F}$ is a subfami...

Given a real Banach space X, we show that the Nehari manifold method can be applied to functionals which are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{d...

In this paper, we investigate power-bounded operators, including surjective isometries, on Banach spaces. Koehler and Rosenthal asserted that an isolated point in the spectrum of a surjective isometry on a Banach space lies in the point spectrum, with the corresponding eigenspace having an invariant complement. However, they did not provide a detai...

This paper deals with an optimal control problem for a chemotaxis system proposed in Luca et al. (Bull Math Biol 65(4):693–730, 2003) describing the aggregation of microglia observed in Alzheimer’s disease. In this model, the movement of cells is directed in response to two chemical signal substances, both produced by the cells, one acting as a che...

We address a question by Henry Towsner about the possibility of representing linear operators between ultraproducts of Banach spaces by means of ultraproducts of nonlinear maps.We provide a bridge between these “accessible” operators and the theory of twisted sums through the so-called quasilinear maps. Thus, for many pairs of Banach spaces X and Y...

Let the abstract fractional space–time operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\partial _t + A)^s$$\end{document} be given, where \documentclass[12pt]...

We present a new characterization of Q-point ultrafilters and use it to optimize the result of Avilés, Martı́nez-Cervantes, and Rueda Zoca linking the existence of L-orthogonal sequences and L-orthogonal elements in Banach spaces via ultrafilter limits.

This research examines the Hyers–Ulam stability of norm-additive functional equations expressed as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{aligned}& \|\...

We address a question by Henry Towsner about the possibility of representing linear operators between ultraproducts of Banach spaces by means of ultraproducts of nonlinear maps. We provide a bridge between these "accessible" operators and the theory of twisted sums through the so-called quasilinear maps. Thus, for many pairs of Banach spaces $X$ an...

The generalization of BVPs always covers a wide range of equations. Our choice in this research is the generalization of Caputo-type fractional discrete differential equations that include two or more fractional $q$-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, includin...

We study the obstructions to coarse universality in separable dual Banach spaces. We prove an `asymptotic linearization' theorem for nonlinear maps into Banach spaces and use it to give streamlined proofs of several results in the literature. We also prove coarse non-universality of several classes of dual spaces, including those with conditional s...

The farming of animals is one of the largest industries, with animal food products, milk, and dairy being crucial components of the global economy. However, zoonotic bacterial diseases, including brucellosis, pose significant risks to human health. The goal of this research is to develop a mathematical model to understand the spread of brucellosis...

The aim of this article is to introduce and study a new class of fractional integro nonlocal boundary value problems involving the p-Laplacian operator and generalized fractional derivatives. The existence of solutions in Banach spaces is investigated with the aid of the properties of Kuratowski’s noncompactness measure and Sadovskii’s fixed-point...

In recent years, many researchers have studied the fixed points of generalized $ \alpha $-nonexpansive (GAN) mappings, yet there has been limited research on multi-valued GAN mappings. In this paper, we focused on the class of multi-valued GAN mappings in the context of Banach spaces. We introduced a novel iterative process to find fixed points of...

We show that if \(p>1\) every subspace of \(\ell _p(\Gamma )\) is an \(\ell _p\)-sum of separable subspaces of \(\ell _p\), and we provide examples of subspaces of \(\ell _p(\Gamma )\) for \(0<p\le 1\) that are not even isomorphic to any \(\ell _p\)-sum of separable spaces, notably the kernel of any quotient map \(\ell _p(\Gamma )\rightarrow L_1(2^...

Building upon the interpolative classical results of D. Achour, P. Rueda, and R. Yahi for Lipschitz ideals we define the interpolative fuzzy Lipschitz ideal concept for fuzzy Lipschitz operators between fuzzy metric spaces and complete fuzzy normed spaces which is a natural generalization of the notion of absolutely (crisp) Lipschitz (p, θ)-summing...

This paper introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational problems, including standard ones. To carry out the process effectively, we utilize specialized sets known as radial...

In this article, we introduce and study the notion of disjoint topologically super-recurrent operators for finitely many operators acting on a complex Banach space. As an application, we characterize the disjoint topological super-recurrence of finitely many different powers of unilateral and bilateral weighted shifts.

Consider two infinite dimensional complex Banach spaces X and Y. The operator matrix M N is defined on X ⊕ Y by M N = M 1 N 0 M 2 , where M 1 ∈ L(X), M 2 ∈ L(Y), and N ∈ L(Y, X). The central focus of this manuscript revolves around the examination of the relation between certain spectral properties of the operator matrix M N and those of their diag...

In the literature surrounding the theory of Banach spaces, considerable effort has been invested in exploring the conditions on a Banach space X that characterise X as being an inner product space or as a linearly isomorphic copy of a Hilbert space. On the other hand, a different theory emerges when the class of Banach spaces is looked upon as a Li...

A Hilbert space operator $T$ is called $n$-paranormal and $*$-$n$-paranormal if $\|Tx\|^n \leq \|T^nx\| \cdot \|x\|^{n-1}$ and $\|T^*x\|^n \leq \|T^nx\| \cdot \|x\|^{n-1}$, respectively. Let $\mathfrak{P}(n)$ and $\mathfrak{S}(n)$ be the sets of all $n$-paranormal operators and $*$-$n$-paranormal operators, respectively. In this paper we study and...

In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily extended to non-autonomous Hamilton-Jacobi equations in Banach spaces. The main tool is the regularizing property...

By the generalizing the extension of the continuous theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence-solutions to the boundary value problems for a class of p-Laplacian equations. Finally an example is given to illustrate our results.

Given 1 < p, r < ∞ and 0 ≤ σ < 1 such that 1/r + (1 − σ)/p * = 1, we study the Banach normalized Bloch ideal (D B p,σ (D, X), d B p,σ) formed by all strongly (p, σ)-absolutely continuous Bloch maps from the complex unit open disc D into a complex Banach space X. Characterizations of such Bloch maps are established in terms of: (i) Pietsch dominatio...

Recently we have presented a unified approach to two classes of Banach spaces defined by means of variations (Waterman spaces and Chanturia classes), utilizing the concepts from the theory of ideals on the set of natural numbers. We defined correspondence between an ideal on the set of natural numbers, a certain sequence space and related space of...

The purpose of this paper was considering the impulsive fractional differential system with time delay. We investigated the existence of solution corresponding to the regulator in the admissible regulator set describing by the compact semigroup on Banach space. The result was applied to nonlinear fractional heat equation.

We prove some equivalence results between limit theorems for sequences of $(\ell)$-group-valued measures, with respect to order ideal convergence. A fundamental role is played by the tool of uniform ideal exhaustiveness of a measure sequence already introduced for the real case or more generally for the Banach space case in our recent papers, to ge...

In this paper, we study the numerical solution of a type of system of mixed nonlinear variational inequalities in a Banach space. Using the properties of $\eta-$proximal mapping, we construct some iterative algorithms for solving systems of mixed nonlinear variational inequalities. Moreover, we establish the convergence theorems for the proposed nu...

In this paper, we mainly study calmness and strong calmness of closed multifunctions over constraint sets in Banach spaces. In terms of tangent cones, normal cones and coderivatives, we provide some dual necessary/sufficient conditions ensuring calmness over constraint sets. In particular we proved a dual characterization for strong calmness of a c...

Fast-growing forest plantations hold significant promise for capturing carbon and are essential in the fight against global warming. In this study, we develop a model to simulate the dynamics of carbon adsorption in rapidly expanding plantations, accounting for the effects of forest burning and biomass growth through fractional operators. To ensure...

We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (Electron J Probab 21:1–53, 2016), to the case of cylindrical martingale-valued measures that are allowed to have...

This article provides an extended and critically refined exploration of the classical theory of existence and uniqueness for Ordinary Differential Equations (ODEs), as well as its modern expansions and applications. We begin with the fundamental Picard-Lindelöf theorem, examining the roles of continuity and Lipschitz conditions and highlighting the...

In this paper, we study convergence of Jungck-Schaefer iterative scheme to the common fixed point of generalized enriched contractions. Some novel general class of enriched contractive definitions called enriched-Jungck contractions are presented and we study the existence and uniqueness of common fixed points for these class of mappings in Banach...

In this paper, we introduce ωn-symmetric polynomials associated with the finite group ωn, which consists of roots of unity, and groups of permutations acting on the Cartesian product of Banach spaces ℓ1. These polynomials extend the classical notions of symmetric and supersymmetric polynomials on ℓ1. We explore algebraic bases in the algebra of ωn-...

The study of systems of ODE is one of the part of investigations in modern analysis and its applications. Unlike Cauchy problems, the solutions to inhomogeneous boundary-value problems for differential systems may not exist and/or may not be unique. Therefore, the question about the solvability character of such problems is fundamental for the theo...

Let $T$ be a power-bounded linear operator on a Hilbert space $X$, and let $S$ be a bounded linear operator from another Hilbert space $Y$ to $X$. We investigate the non-exponential rate of decay of $\|T^nS\|$ as $n \to \infty$. First, when $X = Y$ and $S$ commutes with $T$, we characterize the decay rate of $\|T^nS\|$ by the growth rate of $\|(\la...

In the paper we introduce new norm derivative mappings and the corresponding orthogonality relations induced by it. We show that this notion is useful in the characterization of inner product spaces, characterization of smooth Banach spaces, Birkhoff orthogonality. We prove also some useful computational formulations.

This study presents a novel and efficient iterative approach to approximating the fixed points of contraction mappings in Banach spaces, specifically approximating the solutions of nonlinear fractional differential equations of the Caputo type. We establish two theorems proving the stability and convergence of the proposed method, supported by nume...

In this paper, we prove the existence and uniqueness of the weak solution of a system of nonlinear equations involved in the mathematical modeling of cancer tumor growth with a non homogeneous divergence condition. We also present a new concept of generalized differentiation of non linear operators : C-differentiability. Through this notion, we als...

The aim of this work is to study the existence of a periodic solutions of differential equations $\frac{d^{4} }{ dt^{4} }x(t) = Ax(t) + f(t)$. Our approach is based on the M-boundedness of linear operators, Fourier type, $B^{s}_{p, q}$-multipliers and Besov spaces.

In this chapter, we introduce some terminology and notation. We also describe the standard Banach spaces contained in the product of real lines. Because of interest, some minor topics are also described even if those won’t be use hereafter.

In this paper, we introduce and study the extended Newton-type method for solving generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\Omega\subseteq\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable in a neighborhood $\Omega$ of a point $\bar{x}$ in $\mathcal X$, $g:\Omega\subseteq \mathcal X\to \mathcal Y$ is linear and differentia...

Optimal control problems governed by primal and dual evolution macro-hybrid mixed variational state inclusions, in reflexive Banach spaces, are studied. This is a spatially localized macro-hybrid variational version of our mixed optimal control theory published in Appl. Math. Optim. 68, 2013, 445-473, where the solvability analysis of the state sys...

In this work, we have proposed a Jacobian free iterative vectorial multiparametric family for solving systems of nonlinear equations. The scheme is obtained by replacing the Jacobian matrix by divided difference operator in a family of third and fourth order iterative methods which maintains the convergence order. This way we avoid the expensive in...

In this article we present strong global solutions for the initial value problem in a reflexive Banach space, when the linear part of the corresponding differential evolution equation is Bohl-Bohr or Stepanov almost periodic function, and the displayed operator is infinitesimal generator of (C 0)-semigroup. As an application, we consider a problem...

A “law of large numbers” for consecutive convex hulls of weakly dependent Gaussian sequences {Xn} with the same marginal distribution is extended to the case where the sequence {Xn} has a weak limit. Let 𝔹 be a separable Banach space with a conjugate space 𝔹∗. Let {Xn} be a centered 𝔹-valued Gaussian sequence satisfying two conditions: (1) Xn ⇒ X;...

An exponentially convergent numerical method for solving a differential equation with a right-hand fractional Riemann-Liouville time-derivative and an unbounded operator coefficient in Banach space is proposed and analysed for a homogeneous/inhomogeneous equation of the Hardy-Tichmarsh type. We employ a solution representation by the Danford-Cauchy...

In this paper, the serial killing system is analyzed to construct a scheme for a fractional-order mathematical model having five compartments: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6...

Starting from a unital Banach \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$*$$\end{document}-probability space \documentclass[12pt]{minimal} \usepackage{amsmath} \us...

Let ψ be a Bernstein function in one variable. A. Carasso and T. Kato obtained necessary and sufficient conditions for ψ to have a property that ψ(A) generates a quasibounded holomorphic semigroup for every generator A of a bounded C0-semigroup in a Banach space and deduced necessary conditions as well. We generalize their results to the multidimen...

In this work, we combine measure non-compactness and generalized operators in the setting of partial order Banach spaces to provide some generalized Darbo-type fixed point theorems. We further demonstrate how our findings could potentially apply in reality by establishing that higher-order fractional delay differential equations have solutions. We...

It is proved that the linear space constructed by power base is a banach space under 2-norm by using approximation method. For the Bézier curve--the elements in banach space, the linear combination of the low-order S power base is used to approximate optimal the high-order Bernstein base function. The original Bézier curve is instituted by the line...

Banach spaces play an important role in functional analysis and lead to numerous applications, especially since the norms of the spaces are generated by linear operators and p-integrable norms. In this context, the generalized Hausdorff operator has a deep relevance to various problems in analysis. For suitable kernels, the Hausdorff operator is no...

The well-known theorem asserts that the equation x' = A(ωt)x (ω ∈ Ω) (1) (where (Ω, R, σ) is a compact minimal dynamical system and ωt := σ(t, ω)) can be reduced by a Lyapunov-Perron transformation to the equation x' = B(ωt)x (ω ∈ Ω) with a skew-symmetric matrix B(ω), if all solutions of all equations (1) are bounded on the whole line. In the talk,...

This work explores the equivalence of two sequential properties, $\mathcal{D}$ and $\mathcal{D}'$, for dual Banach spaces under the weak* topology. Property $\mathcal{D}$ ensures that any totally scalarly measurable function is also scalarly measurable, while property $\mathcal{D}'$ states that every weakly* sequentially closed subspace of $X^*$ is...

In this paper, we study a system of nonlinear tempered fractional differential equations with multi-point coupled boundary conditions. By applying the properties of Green’s function and the operator and combining the method of matrix analysis, we obtain the corresponding Lyapunov inequalities under two Banach spaces. And, we have compared two Lyapu...

We use the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document}-linearity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasys...

This paper focuses on one-parameter semigroups of ρ-nonexpansive mappings Tt:C→C, where C is a subset of a modular space Xρ, the parameter t ranges over [0,+∞), and ρ is a convex modular with the Fatou property. The common fixed points of such semigroups can be interpreted as stationary points of a dynamic system defined by the semigroup, meaning t...

We present a new method for solving variational inequality problems (VIPs) based on double inertial terms with a modified subgradient extragradient self-adaptive step size method. Our proposal utilizes double inertial acceleration to improve convergence behavior and stability in solving VIPs. Strong convergence theorems for the proposed algorithms...

In this paper, we introduce five two‐parameter B$\mathbf {B}$‐valued martingale Hardy–Lorentz–Karamata spaces and establish some atomic decomposition theorems via atomic martingales as well as atomic functions. With the aid of atomic decompositions, we obtain some martingale inequalities and characterize the duals of these spaces. Our conclusions s...

In this paper, we developed a new standby system that combines a retrial strategy with multiple working vacations, and we performed a dynamic analysis of the system. We investigated its well−posedness and asymptotic behavior using the theory of the C0−semigroup in the functional analysis. First, the corresponding model was transformed into an abstr...

We apply Pisier’s inequality to establish the stability property of nonsurjective coarse isometries from a Banach space to a uniformly convex space. Making use of this result, we extend some known conclusions on ε,p isometries of Hilbert spaces and Lq spaces.

This article is dedicated to study the existence and uniqueness of solutions for a non local boundary value problem of Caputo-type Hadamard hybrid fractional integro-differential equations in Banach space, the recent researches considered the study of differential equations of Caputo-type Hadamard hybrid fractional integro-differential equations wi...

A local and a semi-local convergence analysis are presented for the Kurchatov-type method to solve numerically nonlinear equations in a Banach space. The method depends on a real parameter. By specializing the parameter, we obtain methods already studied in the literature under different types of conditions, such us Newton’s, and Steffensen’s, and...

The convergence of two-step iterative methods of third and fourth order of convergence are studied under weaker hypotheses than in earlier works using our new idea of the restricted convergence region. This way, we obtain a finer semilocal and local convergence analysis, and under the same or weaker hypotheses. Hence, we extend the applicability of...

In this article, we investigate the optimal feedback control for a class of damping second-order evolution inclusions with Clarke’s subdifferential type in a separable reflexive Banach spaces. First, the existence of a mild solution is identified for the suggested second-order differential inclusion with the notions of generalized Clarke’s subdiffe...

We consider generators of positive \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_0$$\end{document}-semigroups and, more generally, resolvent positive operators A on...

This work develops a computational framework for proving existence, uniqueness, isolation , and stability results for degree d, real analytic, unimodal functions fixed by m-th order Feigenbaum-Cvitanović renormalization operators. Here the order m of the operator refers to the number of function compositions involved in its definition. The degree d...

Let $r,s \in [2,\infty]$ and consider the Navier-Stokes equations on $\mathbb{R}^3$. We study the following two questions for suitable $s$-homogeneous Banach spaces $X \subset \mathcal{S}'$: does every $u_0 \in L^2_\sigma$ have a weak solution that belongs to $L^r(0,\infty;X)$, and are the $L^r(0,\infty;X)$ norms of the solutions bounded uniformly...

This paper proposes an iterative algorithm for the search for common fixed points of two mappings. The properties of approximation and convergence of the method are analyzed in the context of Banach spaces. In particular, this article provides sufficient conditions for the strong convergence of the sequence generated by the iterative scheme to a co...

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the Hardy space on the polydisk and half-space. In particular, we show how the framework leads to a procedure to...

The family of finite subsets $s$ of the natural numbers such that $|s|=1+\min s$ is known as the Schreier barrier in combinatorics and Banach Space theory, and as the family of exactly $\omega$-large sets in Logic. We formulate and prove the generalizations of Friedman's Free Set and Thin Set theorems and of Rainbow Ramsey's theorem to colorings of...

In our previous paper we systematized several known equivalent definitions of Fr\'echet (G\^ ateaux) Differentiability Spaces and Asplund (weak Asplund) Spaces. As an application, we extended the classical Mazur's theorem, and also proved that the product of any family of Banach spaces $(E_{\alpha})$ is an Asplund lcs if and only if each $E_{\alpha...

In this paper, we discuss the existence of nonnegative solutions to a fourth order singular boundary value problem at two points. Our result is based on a recent Birkho -Kellogg type xed point theorem developed on translates of a cone on a Banach space.

In this paper, we explore the existence, uniqueness, and stability of mild solutions in impulsive differential equations featuring conformable fractional derivatives. Our principal findings leverage fractional semigroup theory, complemented by some fixed-point theorems. Additionally, we provide a practical example to demonstrate the relevance of ou...

This manuscript introduces a generalized operator and presents new Darbo-type fixed point theorems pivotal in the existence theory of integral and differential equations. The significance of these theorems lies in their ability to provide conditions under which solutions to complex mathematical problems can be guaranteed. We establish our results b...

In this paper, we deal with Radon-Nikodým theorems for additive interval multimeasures.

This paper investigates the existence of solutions to the Neumann iterative boundary value problem on time scales for *nth-order* dynamic equations with combined iterative and Sturm-Liouville boundary conditions in Banach space. Utilizing fixed-point theorems and dynamic calculus on time scales, we derive sufficient conditions for the existence of...

In this paper, we prove a superstability theorem for a general functional equation ∑j=1∞ajf(γj(t,s))=h(t)g(s), with the unknown functions g:T→X, h:S→K and f:S→X, such that the series ∑j=1∞f(γj(t,s)) is convergent for every (s,t)∈S×T, where S and T are nonempty sets, and X is a Banach space over a field K, which is either the set of real numbers R o...

For locally convex spaces, we systematize several known equivalent definitions of Fr\'echet (G\^ ateaux) Differentiability Spaces and Asplund (Weak Asplund) Spaces. As an application, we extend the classical Mazur's theorem as follows: Let $E$ be a separable Baire locally convex space and let $Y$ be the product $\prod_{\alpha\in A} E_{\alpha}$ of a...

We introduce the notion of subprojective and superprojective operators and we use them to prove a variation of the three-space property for subprojective and superprojective spaces. As an application, we show that some spaces considered by Johnson and Lindenstrauss are both subprojective and superprojective.

We give new characterizations of the optimal data space for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p(bD,\sigma )$$\end{document}-Neumann boundary value p...

This study presents a novel category of nonconvex functions in Banach spaces, referred to as quasi-lower C2 functions on nonempty closed sets. We establish the existence of solutions for nonconvex variational problems involving quasi-lower C2 functions defined in Banach spaces. To illustrate the applicability of our findings, an example is provided...

Let $n, m\in \mathbb{N}, n, m\geq 2$ and $E$ a Banach space. An element $(x_1, \ldots, x_n)\in E^n$ is called a~norming point of $T\in {\mathcal L}(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and $|T(x_1, \ldots, x_n)|=\|T\|,$ where ${\mathcal L}(^n E)$ denotes the space of all continuous $n$-linear forms on $E.$ For $T\in {\mathcal L}(^n E),$ we define $...

Let \( \mathcal{L}_1 \) denote the subspace of \( L_1(\mathbb{R}) \) consisting of the restrictions to \( \mathbb{R} \) of entire functions of exponential type at most \( \pi \), equipped with the \( L_1(\mathbb{R}) \)-norm. In this paper, we describe the dual space \( \mathcal{L}_1' \), showing that it is isomorphic to the Banach space \( \text{BM...

The problem of Ulam stability for equations can be stated in terms of how much the mappings satisfying the equations approximately (in a sense) differ from the exact solutions of these equations. One of the best known results in this area is the following: Let g be a mapping from a normed space V into a Banach space B. Let ξ≥0 and t≠1 be fixed real...

Let us consider framing transitive structure of pseudo-group deformation of differential varieties by homogeneous simutataeneous equations, naturally, of additive type. It is equivalent with approximation property theorem called Pelczynski's theorem on given bases in some Banach spaces. For an inequality of n-dimensional matrices: AX ≤ BY where X a...

For the constructive analysis of locally Lipschitzian system of non-linear differential equations with mixed periodic and two-point non-linear boundary conditions, a numerical-analytic approach is developed, which allows one to study the solvability and construct approximations to the solution. The values of the unknown solution at the two extreme...

The aim of this paper is studying the remotely almost periodic solutions of ordinary differential equations in Banach spaces of the form x ′ = A(t)x + f (t) + F (t, x) with remotely almost periodic coefficients if the linear equation x ′ = A(t)x satisfies the condition of exponential trichotomy and nonlinearity F is sufficiently "small".

We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial value problems with temporal discretization, and various infinite dimensional Banach spaces which are ubiquitou...