# Mohammad MursaleenAligarh Muslim University | AMU · Department of Mathematics

Mohammad Mursaleen

Ph.D.

## About

675

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11,660

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Citations since 2016

Introduction

Additional affiliations

February 1982 - present

February 1982 - present

## Publications

Publications (675)

The present work focuses on the statistical Euler summability,
Euler statistical convergence, and Euler summability of sequences
of fuzzy real numbers via the generalized fractional difference
operator. We make an effort to establish some relations between
different sorts of Euler convergence. Further, we discuss the
fuzzy continuity and demonstrat...

In the present article, we introduced almost [Formula: see text]-statistical convergence of complex uncertain sequences in all five aspects of uncertainty viz., almost surely, mean, measure, distribution and uniformly almost surely. Further, with the aid of interesting examples and diagram we investigated some interrelationships among these uncerta...

In this paper, we determine the upper and lower bounds for the norm of lower triangular matrix operators on Ces\`{a}ro weighted fractional difference sequence spaces of modulus functions. We consider the matrix operators acting between and and identify their bounds and vice-versa. We also investigate the same characteristics for N\"{o}rlund and wei...

In this article, we found an undesirable feature in the theory of summability; that is, the Fourier series of 2π$$ 2\pi $$‐periodic functions is uniformly convergent to the functions via the Ceàsro mean. However, it does not preserve the uniform convergence for the arbitrary periodic functions. To overcome this limitation, the objective of the pape...

In this work, we first introduce the concept of double sequence space \(2^c(\triangle )\). Then, we construct a Hausdorff measure of noncompactness on this space. Furthermore, by employing this measure of noncompactness we discuss the existence of solutions for infinite systems of third-order three-point boundary value problem in the double sequenc...

The growth of photovoltaic (PV) in developing countries remains a major challenge due to a lack of clarity on the performance of the grid-connected PV system. This paper illustrates some of the key features of the operating performance of the 81.9 kWp PV system installed on the roof of academic buildings. Real-time data was monitored over 12 months...

This article aims to study the existence of the solutions to the infinite system of Hilfer fractional differential equations in tempered sequence spaces. We look for a solution in Banach tempered sequence spaces that is more abstract than classical sequence space. Our approach to studying solvability is using the Meir-Keeler condensing operator. Fi...

In this research study, we investigate the existence and uniqueness of solutions for a coupled multiorder system of fractional differential equations involving coupled integro-differential boundary conditions in the Riemann–Liouville setting. The presented results are obtained via classical Banach principle along with Leray–Schauder and Krasnosel’s...

In this paper, we obtain some inequalities involving norm and essential norm of weighted differentiation composition on Bergman spaces with admissible Békollé weights.

In this paper we attempt to define axiomatic measures of non-compactness for Sobolev spaces of integer order \( W^{n,p}(\Omega )\), where \(\Omega \subset \mathbb {R}^{d}\) (which is equivalent to \(\Omega \) being any set of infinite measure). We consider two cases, one with \(\Omega \) being an open subset with finite measure, and another when \(...

This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via ( p , q ) \left(p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigat...

In this paper we study a notion called (E, 1)(C, 1)−weighted statistical convergence and prove a Korovkin type approximation theorem. The rate of convergence for weighted statistical convergence is obtained. In the last section we also give Voronovskaya and Grüss‐Voronovskaya type theorems and some illustrative numerical examples

In this paper Phillips type Bernstein operators (Bk,qsf)(s,t), (Bl,qtf)(s,t), their product and Boolean sum based on q-integer have been introduced on square with one and two curved side. Their interpolation properties, order of accuracy and remainders of the approximation formula for corresponding operators using modulus of continuity and Peano’s...

The recent elevation of cases infected from novel COVID-19 has placed the human life in trepidation mode, especially for those suffering from comorbidities. Most of the studies in the last few months have undeniably raised concerns for hypertensive patients that face greater risk of fatality from COVID-19. Furthermore, one of the recent WHO reports...

In this paper, we apply the notion of B-summability to define a more general case of ideal convergence. We study several properties of this new summability method.

Although robotic vision systems offer a promising technology solution for rapid and reconfigurable in-process 3D inspection of complex and large parts in contemporary manufacturing, measurement accuracy poses a challenge for its wide deployment. One of the key issues in adopting a robotic vision system is to understand the extent of its measurement...

We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain sequence spaces, in solving infinite systems of integral equations in some sequence spaces. We also presen...

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate the stability results by using the Hyers method in modular space for quartic functional equations without using the Fatou property, without using the Δb-condition and without using both the Δb-condition and the Fatou...

In this chapter we present a brief survey of theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We describe some applications in the solvability of infinite systems of differential equations in classical sequence spaces.

In this paper, the King’s type modification of (p, q)-Bleimann-Butzer and Hahn operators is defined. Some results based on Korovkin’s approximation theorem for these new operators are studied. With the help of modulus of continuity and the Lipschitz type maximal functions, the rate of convergence for these new operators are obtained. It is shown th...

The goal of this paper is to obtain the spectra and fine spectra of the matrix Δ 3 a b $\begin{array}{} \displaystyle \Delta_{3}^{ab} \end{array}$ on the Hahn space. Also, we explore some ideas of how to study the problem for a general form of the matrix, namely, the matrix Δ n a b $\begin{array}{} \displaystyle \Delta _{n}^{ab} \end{array}$ where...

We present a generalization of Darbo's fixed point theorem in this article, and we use it to investigate the solvability of an infinite system of fractional order integral equations in ℓ p (1 ≤ p<∞) space. The fundamental tool in the presentation of our proofs is the measure of noncompactness (mnc) approach. The suggested fixed point theory has the...

In this article, a one-to-one correspondence between the set of all one-parameter semigroup of holomorphic self-mappings of the upper-half plane Π+ and the set of all strongly continuous one-parameter semigroup of composition operators on vector-valued Hardy space of the upper-half plane is established.

In this paper generalized Kantorovich operators are constructed using Lototsky-Bernstein basis functions on unit interval. An approximation of continuous functions by these sequence of operators has been established based on Korovkin’s theorem. Finally, we prove that this sequence of operators Dμ(f;x) converges to f∈Lp[0,1] in ‖.‖p.

The Department of Mathematics Education at Tishk International University invites you to an International Workshop titled, 1st International Workshop on Global Contributions to Mathematical Sciences; themed “Operator theory and its interdisciplinary applications.”
The workshop on Global Contributions to Mathematical Sciences is the maiden internat...

The main concern of this article is to acquire some approximation properties of a new class of Bernstein polynomials based on Bézier basis functions with shape parameter λ ∈ [−1,1]. We prove Korovkin type approximation theorem and estimate the degree of convergence in terms of the modulus of continuity, for the functions belong to Lipschitz type cl...

In this article, we construct (p, q)-analogue C(p, q) of Cesàro matrix C1 of order 1 and study its properties. We introduce (p, q)-Cesàro sequence spaces Xsp,q and X∞p,q generated by the domain of matrix C(p, q) in the spaces ℓs and ℓ∞, respectively. We study some topological properties and inclusion relations, obtain Schauder basis of Xsp,q and α-...

In this study, we give another generalization of second order backward difference operator ∇2 by introducing its quantum analog ∇q2. The operator ∇q2 represents the third band infinite matrix. We construct its domains c0(∇q2) and c(∇q2) in the spaces c0 and c of null and convergent sequences, respectively, and establish that the domains c0(∇q2) and...

We study the following fractional boundary value problem:
\begin{footnotesize}\begin{equation*}\label{1.1}\begin{cases} D^{\ell}\upsilon(\jmath)+f(\jmath,\upsilon(\jmath))=0,\quad \ell\in(1,2],\quad 0<\jmath<+\infty,\ &\ \\ \upsilon(0)=0,\quad D^{\ell-1}\upsilon(\infty)=\lambda\int_{0}^{\tau} \upsilon(\jmath)d\jmath. &\ \\
\end{cases}\end{equation*...

In this paper, we discussed a regular summability method called q -statistical convergence. Two new sequence spaces m∗q and s∗q are also obtained. A condition for a q-statistically convergent sequences to be q-Cesàro summable is given. Necessary and sufficient conditions for real sequences and the sequences in m∗q to be q-statistical convergent are...

In this article, we consider a bivariate Chlodowsky type Szász–Durrmeyer operators on weighted spaces. We obtain the rate of approximation in connection with the partial and complete modulus of continuity and also for the elements of the Lipschitz type class. Moreover, we examine the degree of convergence with regard to the weighted modulus of cont...

In this paper, we have studied post-quantum analogue of Appell type polynomials ((p, q)-Appell polynomials) from determinantal aspect using the definition of post-quantum analogue of Appell type polynomials from Sadjang (Anal Math 45:583, 2019). Some basic properties for post-quantum analogue of Appell polynomials have been established. Further 2D...

In this paper, we define concept of approximate fixed point property of a function and a set in intuitionistic fuzzy normed space. Furthermore, we give intu-itionistic fuzzy version of some class of maps used in fixed point theory and investigate approximate fixed point property of these maps.

Our aim is to define modified Szász type operators involving Charlier polynomials and obtain some approximation properties. We prove some results on the order of convergence by using the modulus of smoothness and Peetre's K-functional. We also establish Voronoskaja type theorem for these operators. Moreover, we prove a Korovkin type approximation t...

In this paper, we extend the properties of rational Lupa?-Bernstein blending functions, Lupa?-B?zier curves and surfaces over arbitrary compact intervals [?,?] in the frame of post quantum-calculus and derive the de-Casteljau?s algorithm based on post quantum-integers. We construct a two parameter family as Lupa? post quantum Bernstein functions ov...

We construct Kantorovich variant of generalized Sz?sz-Mirakjan operators whose construction depends on a continuously differentiable, increasing and unbounded function ?. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

In this paper, we obtain the results on the degree of convergence of a function of Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund \begin{document}$ (D^{h}_{g}N^{a,b}) $\end{document} transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main...

This article deals with shape preserving and local approximation properties of post-quantum Bernstein bases and operators over arbitrary interval \begin{document}$ [a, b] $\end{document} defined by Khan and Sharma (Iran J Sci Technol Trans Sci (2021)). The properties for \begin{document}$ (\mathfrak{p}, \mathfrak{q}) $\end{document}-Bernstein bases...

In the present paper, we consider the Kantorovich modification of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing and unbounded function $\rho$. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

This paper deals with Lupaş post quantum Bernstein operators over arbitrary closed and bounded interval constructed with the help of Lupaş post quantum Bernstein bases. Due to the property that these bases are scale invariant and translation invariant, the derived results on arbitrary intervals are important from computational point of view. Approx...

The main purpose of this research article is to construct a Dunkl extension of $(p,q)$ ( p , q ) -variant of Szász–Beta operators of the second kind by applying a new parameter. We obtain Korovkin-type approximation theorems, local approximations, and weighted approximations. Further, we study the rate of convergence by using the modulus of continu...

The notion of statistical convergence was extended to $\mathfrak{I}$ I -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the notion of statistically $\mathfrak{A}^{\mathfrak{I}}$ A I -Cauchy and statistically $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ A I ∗ -Cauchy summability vi...

The motive of the present paper is to construct q-Phillips operators generated by the parametric extension of exponential function by including the parameter \(\zeta \in \big [ -\frac{1}{2}, \infty )\). First we give the basic estimates to obtain their central moments and then study the Korovkin’s-type approximation theorems. Moreover, we investiga...

In this work, we study characterizations of some matrix classes $(\mathcal{C}^{(\alpha )}(\ell ^{p}),\ell ^{\infty })$ ( C ( α ) ( ℓ p ) , ℓ ∞ ) , $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c)$ ( C ( α ) ( ℓ p ) , c ) , and $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c^{0})$ ( C ( α ) ( ℓ p ) , c 0 ) , where $\mathcal{C}^{(\alpha )}(\ell ^{p})$ C ( α ) ( ℓ p )...

The objective of the present exploration is to examine the nanoliquid flow amid two horizontal infinite plates. The lower plate is stretchable and permeable. The uniqueness of the flow model is assimilated with the Hall effect, variable thermal conductivity, thermal radiation, and irregular heat source/sink. Transmission of mass is enhanced with th...

Let N denote the set of all positive integers and N0 = N [ f0g. For m 2 N, let Bm =
fz 2 Cm : jzj < 1g be the open unit ball in the mdimensional Euclidean space Cm. Let H(Bm) be
the space of all analytic functions on Bm. For an analytic self map x = (x1, x2, . . . , xm) on Bm and
f1, f2, f3 2 H(Bm), we have a product type operator Tf1,f2,f3,x whic...

The incomplete gamma function Γ( a , u ) is defined by
Γ ( a , u ) = ∫ u ∞ t a − 1 e − t d t , $$\Gamma(a,u)=\int\limits_{u}^{\infty}t^{a-1}\textrm{e}^{-t}\textrm{d} t,$$
where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix P ( μ ) = ( p n k μ ) $\mathfrak{P}(\mu)=(p^{\mu}_{nk})$ given by
p n k μ = n ! Γ ( n...

In the present note, we discuss the convergence of the difference sequences defined by Kızmaz (Can Math Bull 24(2):169–176, 1981), Et and Çolak (Soochow J Math 21(4):377–386, 1995), Malkowsky et al. (Acta Math Sin (English Series) 23(3):521–532, 2007), Başar (Summability theory and its applications, Monographs. Bentham Science Publishers, İstanbul,...

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having...

A correction to this paper has been published: https://doi.org/10.1007/s13324-021-00546-9

This investigation aims to explore the temperature-dependent variable characteristics of viscosity, and thermal conductivity with modified Fourier law in a nanofluid flow over a rotating disk. The uniqueness of the envisioned mathematical model is improved with the additional impacts of the chemical reaction, non-uniform source/sink, and convective...

In this study, we deal with some new vector valued multiplier spaces SGh(∑kzk) and SwGh(∑kzk) related with ∑kzk in a normed space Y. Further, we obtain the completeness of these spaces via weakly unconditionally Cauchy series in Y and Y∗. Moreover, we show that if ∑kzk is unconditionally Cauchy in Y, then the multiplier spaces of Gh-almost converge...

In this research, we introduce the fractional Copson matrix and define the associated sequence spaces. We investigate the inclusion relations, dual spaces and matrix transformations of these new sequence spaces. Moreover, investigating the compactness of matrix operators and obtaining the norm of this matrix on the difference sequence spaces are an...

In this article, applying the concept of measure of noncompactness, some fixed point theorems
in the Frechet space ´ L∞(G) (where G ⊆ Rω) have been proved. We handle our obtained consequences to
inquiry the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend
some famous related results in the literatur...

n this paper, we give a new generalization of Darbo’s fixed point theorem of integral type. An application for the solvability of nonlinear fractional integral equations is given to illustrate our result.

. In this paper, we introduce a nonlinear inequality based on four self-mappings. We
give necessary conditions which ensure the existence of a common fixed point of four selfmappings satisfying said inequality defined in S´-metric spaces. A common fixed point problem
is discussed. We set up an example to elucidate our main result. Moreover, the exi...

The present paper emphasises on equi-statistical convergence, pointwise statistical convergence and uniform statistical convergence for a sequence of real-valued functions by using deferred Cesàro and deferred Euler statistical convergence and obtain various implicative results with supporting examples. We make an effort to demonstrate Korovkin-typ...

In this article, we present some fixed point and coupled fixed point theorems adapted from the notion of F-contraction mappings in Banach spaces (B.S.) via the measure of noncompactness (M.N.C). Then we define and present a new class of generalized F-contractions, to upgrade some results of Falest and Latrach (Bull Bell Math Soc Simon Stevin 22:797...

In this study, we introduce new BK-spaces bsr,tp,q and b∞r,tp,q derived by the domain of p,q-analogue Br,tp,q of the binomial matrix in the spaces ℓs and ℓ∞, respectively. We study certain topological properties and inclusion relations of these spaces. We obtain a basis for the space bsr,tp,q and obtain Köthe-Toeplitz duals of the spaces bsr,tp,q a...

In this paper we generalize the space ℓˆk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{\ell }_{k}$\end{document} of absolutely almost convergent series (J. Math....

Consumer behaviour is one of the most important and complex areas of research. It acknowledges the buying behaviour of consumer clusters towards any product, such as life insurance policies. Among various factors, the three most well-known determinants on which human conjecture depends for preferring a product are demographic, economic and psychogr...

In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also consid...

The purpose of the paper is to introduce new analogues of Lupaş type Bernstein operators Bm,quf(u,v) and Bn,qvf(u,v), their products Pmn,qf(u,v) and Qnm,qf(u,v) and their Boolean sums Smn,qf(u,v) and Tnm,qf(u,v)on triangle Th, which interpolate a given function on the some edges and at the vertices of triangle using quantum analogue. Based on Peano...

In this paper generalized Kantorovich Operators are constructed using Lototsky-Bernstein basis functions on unit interval. Approximation of continuous functions by these sequence of operators has been established based on Korovkin's theorem. It has been shown that these sequence of generalized Kantorobich Operators converges to functions $f$ belong...

Congestive heart failure is among leading genesis of concern that requires an immediate medical attention. Among various cardiac disorders, left ventricular systolic dysfunction is one of the well known cardiovascular disease which causes sudden congestive heart failure. The irregular functioning of a heart can be diagnosed through some of the clin...

In this paper, we intend to form certain estimates and identities for the norm of matrix operator from \(\ell _{r}\)-type binomial fractional difference sequence space into \(c, c_{0}, \ell _{\infty }\) and \(\ell _{1}\) sequences spaces. We obtain the necessary and sufficient conditions for some classes of compact operators on \(\ell _{r}\)-type b...

Recently, due to its numerous applications, the spectra of the bounded operators over Banach spaces have been studied extensively. This work aims to collect some of the investigations on the spectra of difference operators or matrices on the Banach space c in the literature and provide a foundation for related problems. To the best of our investiga...

Tauberian theorem serves the purpose to recuperate Pringsheim’s convergence of a double sequence from its (C, 1, 1) summability under some additional conditions known as Tauberian conditions. In this article, we intend to introduce some Tauberian theorems for fuzzy number sequences by using the de la Vallée Poussin mean and double difference operat...

The main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

The quantum analogue of Bernstein operators Bm,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {B}}_{m,q}$$\end{document} reproduce the linear polynomials wh...

In the present article we study the approximation properties of Phillips operators by q-Dunkl generalization. We construct the operators in a new q-Dunkl form and obtain the approximation properties in weighted function space. We give the rate of convergence in terms of Lipschitz class by initiate the modulus of continuity and finally, we present s...

The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators Bm,qufu,v and Bn,qvfu,v, their products Pmn,qfu,v and Qnm,qfu,v, their Boolean sums Smn,qfu,v and Tnm,qfu,v on triangle Th, which interpolate a given function on the edges, respectively, at the vertices of triangle using quantum analogue. Based on Peano’s t...

The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators ðB u m,q f Þðu, vÞ and ðB v n,q f Þðu, vÞ, their products ðP mn,q f Þðu, vÞ and ðQ nm,q f Þðu, vÞ, their Boolean sums ðS mn,q f Þðu, vÞ and ðT nm,q f Þðu, vÞ on triangle T h , which interpolate a given function on the edges, respectively, at the vertices of...

In this paper, the idea of -bipolar fuzzy -ideals and an -bipolar fuzzy ideals of -algebras is delivered, and their related properties are investigated with the aid of some examples. We also provide the connection between -bipolar fuzzy ideals and bipolar fuzzy ideals and -bipolar fuzzy -ideals and bipolar fuzzy -ideals by way of counterexamples....