Hassen Aydi

Imam Abdul Rahman bin Faisal University

The goal of this paper is to obtain some tripled coincidence point results for generalized contraction mappings in the setting of $ JS $-metric spaces endowed with a partial order. Furthermore, illustrative examples to support the theoretical results and the application are obtained. Finally, some theoretical results are applied to discuss the exis...

The goal of this paper is to present a new class of contraction mappings, so-called $ \eta _{\theta }^{\ell } $-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for $ \eta _{\theta }^{\ell } $-contraction mappings are introduced. Furthermore, to support our results, two examples are provided. F...

Using Atangana-Baleanu ($ AB $) fractional integral operators, we first establish some fractional Hermite-Hadamard-Mercer inclusions for interval-valued functions in this study. In this, some fresh developments of the Hermite-Hadamard inequality for fractional integral operators are presented. A few instances are also given to support our conclusio...

In this work, we initiate the notion of a fuzzy cyclic $ (\alpha, \beta) $-admissibility to establish some fixed point results for contraction mappings involving a generalized simulation function in the class of fuzzy $ b $-metric spaces. We give some illustrative examples to validate the new concepts and obtained results. At the end, we present an...

In this paper, a general framework for the fractional boundary value problems is presented. The problem is created by Riemann-Liouville type two-term fractional differential equations with a fractional bi-order setup. Moreover, the boundary conditions of the suggested system are considered as mixed Riemann-Liouville integro-derivative conditions wi...

This paper explores certain best proximity point expansions for a novel class of non-self-mapping S : P −→ Q and T : Q → P called generalized proximal C-contractions of the first and second kinds. We expose many examples to justify our obtained results. Considerable fixed point results are evolved as a consequence of our main theorems.

The fundamental goal of this paper is to derive common fixed-point results for a sequence of multivalued mappings contained in a closed ball over a complete neutrosophic metric space. A basic and distinctive procedure has been used to prove the proposed results.

Recently, a class of mappings named as couplings was introduced in [U.P.B. Sci. Bull. Series A, 79 (2017), 1-12]. Based on this concept, we introduce symmetric Meir-Keeler couplings and we ensure the existence of strong coupled fixed points. We present some concrete examples to support the obtained results. Furthermore, as an application of our res...

n this paper, we introduce a generalized ∆-implicit locally contractive condition and give some examples to support it and show its significance in fixed point theory. We prove that the mappings satisfying the generalized ∆-implicit locally contractive condition admit a common fixed point, where the ordered multiplicative GM-metric space is chosen...

In this paper, a novel and more general type of sequence of non-linear multivalued mappings as well as the corresponding contractions on a metric space equipped with a graph is initiated. Fixed point results of a single-valued mapping and the new sequence of multivalued mappings are examined under suitable conditions. A non-trivial comparative illu...

Agarwal et al. (2021) established the extension of several fundamental contiguous relations for G B . Our aim in this work is to investigate several properties of differentiation formulas, differential equations, recursion relations, differential recursion relations, confluence formulas, series representations, integration formulas, and infinite su...

In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chos...

The objective of the present research is to establish and prove some new common fuzzy fixed-point theorems for fuzzy set-valued mappings involving Θ-contractions in a complete metric space. For this purpose, a novel integral-type contraction condition is applied to obtain these results. In this way, several useful and classical results have been ge...

The present paper establishes several new integral representations of the Euler type and Laplace type for some Gauss hypergeometric functions of three variables. The main results are obtained by using the properties of Gamma and beta functions. The novel integral representations are carried out through ten hypergeometric functions of three variable...

In this paper, we introduce $ \mathcal{J}_{s; \Omega} $-families of generalized pseudo-$ b $-distances in $ b $-gauge spaces $ (U, {Q}_{s; \Omega}) $. Moreover, by using these $ \mathcal{J}_{s; \Omega} $-families on $ U $, we define the $ \mathcal{J}_{s; \Omega} $-sequential completeness and construct an $ F $-type contraction $ T:U\rightarrow U $....

By combining the concept of orthogonality and the Geraghty type contraction, we give some fixed point results in the class of O-metric spaces. Our obtained results extend the existing results in the literature. We also resolve an ordinary type differential equation.

The aim of the manuscript is to present the concept of a graphical double controlled metric-like space (for short, GDCML-space). The structure of an open ball of the proposed space is also discussed, and the newly presented ideas are explained with a new technique by depicting appropriately directed graphs. Moreover, we present some examples in a g...

The purpose of this manuscript is to present some fixed point results for a Λ-Ćirić mapping in the setting of non-triangular metric spaces. Also, two numerical examples are given to support the theoretical study. Finally, under suitable conditions, the existence and uniqueness of a solution to a general Fredholm integral equation, a Riemann-Liouvil...

This article is based on the concept of partial extended b -metric spaces, which is inspired by the notions of new extended b -metric spaces and partial metric spaces. Fixed point results for single and multivalued mappings on such spaces are also presented. Few examples are also provided to elaborate the concepts.

Inspired by certain study of recursion formulas involving multivariable hypergeo-metric functions [14, 15, 16, 17, 18, 22, 23]. In this article, we introduce five new quadruple hypergeometric functions together with their regions of convergence and then we establish certain recursion relations for these new functions. This enriches the theory of sp...

This paper tackles the topic of conformable Laplace transform. The authors aim at discussing its existence by exploring and providing the kind of functions that possess a conformable Laplace transform. Furthermore, the comparison theorem of conformable improper integrals is presented to further explain and justify the existence of conformable Lapla...

The purpose of this note is to come up with some new directions in fuzzy fixed point theory. To this effect, notions of a C ∗ -algebra-valued fuzzy λ -contraction and related concepts in a convex C ∗ -algebra-valued metric space ( C ∗ -AVMS) are set-up. In line with the view of a Hausdorff distance function, an idea of a distance between two approx...

The article presents a systematic investigation of an extension of the developments concerning $ F $-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of $ F $-contractions to the case of non-linear ($ F $, $ F_{H} $)-dynamic-iterative scheme for Branciari Ćirić type-contractions and prove multi-valued fixed point...

This manuscript was built to generalize Ekeland variational principle for mixed monotone functions in the setting of partially ordered complete metric spaces. The results obtained are applied to give different proofs for tripled fixed points of mixed monotone mappings in the mentioned space by using a variational technique. The results presented in...

Our aim is to prove some new fixed point theorems for a hybrid pair of multivalued α *-dominated mappings involving a generalized Q-contraction in a complete modular-like metric space. Further results involving graphic contractions for a pair of multi-graph dominated mappings have been considered. Applying our obtained results, we resolve a system...

The goal of this manuscript is to obtain some tripled fixed point results under a new contractive condition and triangular property in the context of fuzzy cone metric spaces (F CM-spaces). Moreover, two examples and corollaries are given to validate our work. Ultimately, as applications, the notion of Lebesgue integral is represented by the fuzzy...

The purpose of this paper is to present a new concept of a Banach algebra in a fuzzy metric space (FM-space). We define an open ball, an open set and prove that every open ball in an FM-space over a Banach algebra $ \mathcal{A} $ is an open set. We present some more topological properties and a Hausdorff metric on FM-spaces over $ \mathcal{A} $. Mo...

The present work is about the existence of best proximity points for Prešić type nonself operators in $ b $-metric spaces. In order to elaborate the results an example is presented. Moreover, some interesting formulations of Prešić fixed point results are also established. In addition a result in double controlled metric type space is also formulat...

This article is concerned with a class of contractions in the framework of a fuzzy metric space endowed with a graph. The main results obtained not only broaden but also generalize a number of relevant results in the literature. Particularly, we get some results for cyclic contractions in fuzzy metric spaces. We also consider an integral equation.

In this article, we introduce (Ψ,Φ)-orthogonal interpolative contractions which generalize orthogonal interpolative contractions. We investigate different conditions on the functions Ψ,Φ:(0,∞)→(−∞,∞) to show the existence of fixed-points of set-valued (Ψ,Φ)-orthogonal interpolative contractions. Our fixed point results are improvement of several kn...

This article presents the E -parametric metric space, which is a generalized concept of parametric metric space. After that, the discussion is concerned with the existence of fixed points of single and multivalued maps on E -parametric metric spaces satisfying some contractive inequalities defined by an auxiliary function.

The aim of this manuscript is to present some new fixed point results in complete partially order metric spaces and to derive some extended forms of Suzuki and Banach fixed point theorems via a $ \tau $-distance by applying some new control functions. Our results are extensions of several existing fixed point theorems in the literature. To show the...

In this article, the concept of a Hausdorff fuzzy b-metric space is introduced. The new notion is used to establish some fixed point results for multivalued mappings in G-complete fuzzy b-metric spaces satisfying a suitable requirement of contractiveness. An illustrative example is formulated to support the results. Eventually, an application for t...

This article investigates the existence and uniqueness (EU) of positive solutions to the tripled system of multi-point boundary value problems (M-PBVPs) for fractional order differential equations (FODEs). The topological degree theory technique is employed to derive sufficient requirements for the (EU) of positive solutions to the proposed system....

In the present paper, we study the existence and convergence of the best proximity point for cyclic Θ \Theta -contractions. As consequences, we extract several fixed point results for such cyclic mappings. As an application, we present some solvability theorems in the topic of variational inequalities.

In this paper, we discuss some (coincidence) best proximity point results for generalized proximal contractions and -proximal Geraghty contractions in controlled metric type spaces. To clarify our study, various examples are given and some conclusions are drawn. 1. Introduction and Preliminaries To solve the equation ( is a mapping defined on a su...

Several (generalized) hypergeometric functions and a variety of their extensions have been presented and investigated in the literature by many authors. In the present paper, we investigate four new hypergeometric functions in four variables and then establish several recursion formulas for these new functions. Also, some interesting particular cas...

In this research article, we determine some vertex degree-based topological indices or descriptors of two families of graphs, i.e., and , where is a graph obtained by identifying one of the vertices of with one vertex of . Similarly, a graph formed by joining one of the vertices of with one vertex of is known as the graph. 1. Introduction Around t...

Citation: Sarwar, M.; Ullah, M.; Aydi, H.; De La Sen, M. Near-Fixed Point Results via Z-Contractions in Metric Interval and Normed Interval Spaces. Symmetry 2021, 13, 2320. https://doi.

In this paper, we derive some common α -fuzzy fixed point results for fuzzy mappings under generalized almost $\mathcal{\mathbf{F}}$ F -contractions in the context of a controlled metric space, which generalize many preexisting results in the literature. As an application, we establish some multivalued fixed point results. For justification of our...

The main motive of this study is to present a new class of a generalized k-Bessel–Maitland function by utilizing the k-gamma function and Pochhammer k-symbol. By this approach, we deduce a few analytical properties as usual differentiations and integral transforms (likewise, Laplace transform, Whittaker transform, beta transform, and so forth) for...

In this study, we introduce a property (P) and the generalized interpolative contractions of types I, II, III, and IV. We investigate certain conditions for the existence of fixed points of generalized interpolative contractions. We derive several new results from the main theorems. As an application, we resolve the Urysohn integral equation. 1. I...

In this article, we investigate the existence, uniqueness, and different kinds of Ulam–Hyers stability of solutions of an impulsive coupled system of fractional differential equations by using the Caputo–Katugampola fuzzy fractional derivative. We applied the Perov-type fixed point theorem to prove the existence and uniqueness of the proposed syste...

This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of...

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional...

This paper deals with introducing and investigating a new convex mapping namely, n-polynomial exponentially s-convex. Here, we present some algebraic properties and some logical examples to validate the theory of newly introduced convexity. Some novel adaptations of the well-known Hermite-Hadamard and Ostrowski type inequalities for this convex fun...

The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominated mappings which are generalized V -contractions in modular-like metric spaces. Some theorems using a partial order are discussed and also some useful results to graphic contractions for fuzzy-graph dominated mappings are developed. To explain the vali...

The aim of this manuscript is to establish several finite summation formulas (FSFs) for the generalized Kampé de Fériet series (GKDFS). Moreover, the particular result for confluent forms of Lauricella series in variables and four generalized Lauricella functions are obtained from the finite summation formulas for the GKDFS. 1. Introduction Specia...

The aim of this work is to extend the Geraghty fixed point result motivated by the approach of Wardowski (Fixed Point Theory Appl 2012:94, 2012). Precisely, we introduce the class of Geraghty \(\alpha \)-\(\Gamma -\chi \)-contractions and provide the related fixed point result in (ordered) b-metric spaces. We also derive periodic point results for...

The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established res...

This article is focused on the generalization of some fixed point theorems with Kannan-type contractions in the setting of new extended -metric spaces. An idea of asymptotic regularity has been incorporated to achieve the new results. As an application, the existence of a solution of the Fredholm-type integral equation is presented. 1. Introductio...

In this paper, we prove fixed point theorems using orthogonal triangular -admissibility on orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by the obtained results. An instance to help our outcome is being presented. 1. Introduction One of the most important results of mathematical a...

A remarkably large number of hypergeometric (and generalized) functions and a variety of their extensions have been presented and investigated in the literature by many authors. In this paper, we introduce five new hypergeometric functions in four variables and then establish several recursion formulas for these new functions. Some interesting part...

We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,μ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,μ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Mor...

In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix function. We also obtain some finite matrix and infinite matrix summation formulas for the Kampé de Fériet hypergeometric matrix function. 1. Introduction The theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well...

In this study, we establish some results for strong convergence of a sequence to a common fixed point of a subfamily of a nonexpansive and periodic evolution family of bounded linear operators acting on a closed and bounded subset of a strictly convex Banach space . In fact, we generalized the results from semigroups of the operator to an evolution...

In this paper, we define the notation of admissible hybrid Z-contractions in the setting of extended b-metric spaces, which unifies and generalizes previously existing results in literature. Furthermore, as an application, we discuss Ulam-Hyers stability and well-posedness of a fixed point problem.

Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically,...

Recently, hypergeometric functions of four variables are investigated by Bin-Saad and Younis. In this manuscript, our goal is to initiate a new quadruple hypergeometric function denoted by $X ^{4}_{84}$ , and then, we ensure the existence of solutions of systems of partial differential equations for this function. We also establish some integral re...

We introduce double and triple F -expanding mappings. We prove related fixed point theorems. Based on our obtained results, we also prove the existence of a solution for fractional type differential equations by using a weaker condition than the sufficient small Lipschitz constant studied by Mehmood and Ahmad (AIMS Math. 5:385–398, 2019) and Hanadi...

In this paper, we study the behavior of $L_{ ( \omega,C ) }$ L ( ω , C ) -contraction mappings and establish some results on common fixed circles and discs. We explain the significance of our main theorems through examples and applications.

In this article, we establish some results for convergence in a strong sense to a common fixed point of a subfamily of a nonexpansive evolution family of bounded linear operators on a Hilbert space. The obtained results generalize some existing ones in the literature for semigroups of operators. An example and an open problem are also given at the...

This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, and fixed point results for set-valued fuzzy cone-contraction and for multi-valued fuzzy cone-contraction mappings. We prove a fixed point theorem for multi-valued rational type fuzzy cone-contractions in fuzz...

The purpose of this paper is to provide some fixed-point results for Suzuki and Wardowski-type contraction multivalued mappings in partial symmetric spaces. We give some examples to support and substantiate the developed notions and obtained results. Also, we use one of our main results to establish the existence and uniqueness of the solution for...

Motivated by the ideas of F-weak contractions and F,Rg-contractions, the notion of Fw,Rg-contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings,...

Fuzzy set theory and fuzzy logics are the powerful mathematical tools to model the imprecision and vagueness. In this research, the novel concept of complex Pythagorean fuzzy relation (CPFR) is introduced. Furthermore, the types of CPFRs are explained with appropriate examples such as CPF composite relation, CPF equivalence relation, CPF order rela...

This paper provides two wide classes of contractions, which are obtained by using notions of αsp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha _{s^{p}} $\end{doc...

This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations: μτ...

The aim of this work is to establish results in fixed point theory for a pair of fuzzy dominated mappings which forms a rational fuzzy dominated V-contraction in modular-like metric spaces. Some results via a partial order and using the graph concept are also developed. We apply our results to ensure the existence of a solution of nonlinear Volterr...

In this paper, we introduce the notion of controlled rectangular metric spaces as a generalization of rectangular metric spaces and rectangular b-metric spaces. Further, we establish some related fixed point results. Our main results extend many existing ones in the literature. The obtained results are also illustrated with the help of an example....

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction and F-Khan-type multivalued contraction mappings on a metric space with a graph. At the end, we give an illustrative example.

In this manuscript, we introduce the concept of complex-valued triple controlled metric spaces as an extension of rectangular metric type spaces. To validate our hypotheses and to show the usability of the Banach and Kannan fixed point results discussed herein, we present an application on Fredholm-type integral equations and an application on high...

In this manuscript, we present further extensions of the best approximation theorem in hyperconvex spaces obtained by Khamsi.

In this manuscript, we initiate the concept of rectangular α-G-admissible mappings with respect to β and we consider related type contractions in the setting of G-metric spaces. We provide some fixed point results. Also, some examples are given to support the obtained results.

In this article, we are generalizing the concept of control fuzzy metric spaces by introducing orthogonal control fuzzy metric spaces. We prove some fixed point results in this setting. We provide nontrivial examples to show the validity of our main results and the introduced concepts. An application to fuzzy integral equations is also included. Ou...

Our aim is to establish a tripled fixed and coincidence point result on generalized -algebra-valued metric spaces. We present an example on matrices. At the end, we give an application on integral equations. 1. Introduction The Banach contraction principle (BCP) was considered by Perov [1] on spaces equipped with vector-valued metrics. The result...

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b -metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α -fuzzy fixed point theorems in the context of extended b -metric spaces that generalize Nadler’s fixed point theorem as well as m...

The aim of this manuscript is to introduce the concept of fuzzy b-metric-like spaces and discuss some related fixed point results. Some examples are imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the obtained results, an application is provided to solve a first kind of Fredholm type integral...

In this paper, we introduce the notion of (s, r)-contractive multivalued weakly Picard operators via simulation functions, named as Z_(s,r)-contractions. We present some related fixed point theorems. We investigate data dependence and strict fixed point results. e well-posedness for such operators is also considered. Moreover, we generalize the res...

In this paper, by using certain inverse pairs of symbolic operators introduced by Choi and Hasanov in 2011, we establish several decomposition formulas associated with the Gaussian triple hypergeometric functions. Some transformation formulas for these functions have also been obtained.

The aim of this manuscript is to introduce the concept of fuzzy b-metric-like spaces and discuss some related fixed point results. Some examples are imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the obtained results, an application is provided to solve a first kind of Fredholm type integral...

Recently, Wu in 2018 established interesting results in the framework of interval spaces. He initiated the idea of near-fixed points and proved some related basic results in metric interval, norm interval, and hyperspaces. In 2015, Khojasteh et al. gave the concept of simulation functions and studied some fixed-point results in metric spaces. Motiv...

Partial b-metric spaces are characterised by a modified triangular inequality and that the self-distance of any point of space may not be zero and the symmetry is preserved. The spaces with a symmetric property have interesting topological properties. This manuscript paper deals with the existence and uniqueness of fixed point points for contractio...

In this paper, we introduce the concept of -contractions and prove the existence of fixed points for contravariant mappings on bipolar metric spaces. 1. Introduction and Preliminaries The notion of a metric space has many generalizations in literature. One of the most recent generalizations is that of a bipolar metric space, introduced by Mutlu an...

This paper involves extended b−metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b−metric space. Thereafter, by making consequent use of the fixed...