Erdal Karapinar

Erdal Karapinar

Professor
"Homo homini lupus est!"

About

556
Publications
87,762
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
14,974
Citations
Introduction
Dear colleagues, Thanks to this platform, I responded positively to every article request, spent time, uploaded, and shared my articles. However, I don't find it fair that my related/shared works are not cited in the articles. I know it since several papers have been sent to me as a referee and editor. For example, I introduced the concept of "interpolated contraction" myself.On the other hand, even the articles on interpolation contraction did not cite/refer to my related articles. Is it fair

Publications

Publications (556)
Article
Full-text available
In this article, we conceive the notion of a generalized (α, ψ, q)-Meir-Keeler contractive mapping and then we investigate a fixed point theorem involving such kind of contractions in the setting of a complete metric space via a w-distance. Our obtained result extends and generalizes some of the previously derived fixed point theorems in the litera...
Article
Full-text available
This paper deals with the existence and uniqueness of the mild solution of the fractional integro-differential equations with non-instantaneous impulses and state-dependent delay. Our arguments are based on the fixed point theory. Finally, an example to confirm of the results is provided.
Article
Full-text available
In this paper, we aim to review Meir–Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M-metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers...
Article
Full-text available
In this paper, we investigate contractions in a rational form in the context of the supermetric space, which is a very interesting generalization of the metric space. We consider an illustrative example to support this new result on supermetric space.
Article
Full-text available
Modular metric space is one of the most interesting spaces in the framework of the metric fixed point theory. The main goal of the paper is to provide some certain fixed point results in the context of modular metric spaces and non-Archimedean modular metric spaces. In particular, we examine the existence of interpolative Meir–Keeler contraction ty...
Article
Full-text available
In the paper, the authors present a brief overview and survey of the scientific work by Chinese mathematician Feng Qi and his coauthors.
Article
In recent years, Fixed Point Theory has achieved great importance within Nonlinear Analysis especially due to its interesting applications in real-world contexts. Its methodology is based on the comparison between the distances between two points and their respective images through a nonlinear operator. This comparison is made through contractive c...
Article
This paper investigates the existence and stability of random solutions of a class of Had-amard fractional order functional partial integral equations with random effects in Banach spaces.
Article
Full-text available
In this paper, we obtain new results which have not been encountered before in the literature, in multivalued quasimetric spaces, inspired by Proinov type contractions. We use admissible function as proving theorems. We also give an example that supports our theorems.
Article
Full-text available
The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations with infinite delay. The arguments are based on a random fixed point theorem with stochastic domain combined with the measure of noncompactness.
Article
Full-text available
In this manuscript, we examine both the existence, uniqueness, and the stability of solutions to the boundary value problem (BVP) of Hadamard fractional differential equations of variable order by converting it into an equivalent standard Hadamard (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise co...
Article
Full-text available
In this paper, the notion of hybrid Jaggi-Meir-Keeler type contraction is introduced. The existence of a fixed point for such operators is investigated. The derived results combine and extend a number of existing results in the corresponding literature. Examples are established to express the validity of the obtained results.
Article
Full-text available
In this article, we study some existence and controllability results for two classes of second order functional differential equations with delay and random effects. To begin, we employ a random fixed point theorem with a stochastic domain to demonstrate the existence of mild random solutions. Next, we prove that our problems are controllable. Fina...
Article
Full-text available
In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and Krasnoselskii fixed point theorem. As appli...
Article
Full-text available
One of the most interesting tasks in mathematics is, undoubtedly, to solve any kind of equations. Naturally, this problem has occupied the minds of mathematicians since the dawn of algebra. There are hundreds of techniques for solving many classes of equations, facing the problem of finding solutions and studying whether such solutions are unique o...
Article
Full-text available
In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indic...
Article
Full-text available
This paper deals with the existence and uniqueness results for a class of impulsive boundary value problem for implicit nonlinear fractional differential equations and k-Generalized ψ-Hilfer fractional derivative involving both retarded and advanced arguments. Our results are based on the Banach contraction principle and Schauder's fixed point theo...
Article
Full-text available
In this paper, we aim to revisit some non-unique fixed point theorems that were initiated by Ćirić, first.We consider also some natural consequences of the obtained results. In addition, we provide a simple example to illustrate the validity of the main result.
Article
Full-text available
In this paper, we consider a class of pseudoparabolic equations with the nonlocal condition and the Caputo derivative. Two cases of problems (1–2) will be studied, which are linear case and nonlinear case. For the first case, we establish the existence, the uniqueness, and some regularity results by using some estimates technique and Sobolev embedd...
Article
Full-text available
In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q -difference An illustrative example is given in the last section.
Article
Full-text available
In this paper, we introduce some common fixed point theorems for interpolative contraction operators using Perov operator which satisfy Suzuki type mappings. Further, some results are given. These results generalize several new results present in the literature.
Article
Full-text available
In this paper, we introduce the notions of Z Γ −contractions and Suzuki Z Γ-contractions via Γ−simulation functions. By using these new contractions, we extend and unify several existing fixed point results in the corresponding literature. We also show that the recently defined notion of L −simulation function is an special case of Z Γ −contraction...
Article
The purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces.
Article
Full-text available
In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example t...
Article
In this short manuscript, we revisit the renowned contraction’s of Meir-Keeler by involving the interpolation theory in the context of complete metric space. We provide a simple example to illustrate the validity of the observed result.
Article
Full-text available
In this paper, we establish some point of ϕ-coincidence and common ϕ-fixed point results for two self-mappings defined on a metric space via extended CG-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we dedu...
Article
The aim of the present work is to study a large class of \(\psi -\)Hilfer fractional differential equation of Pantograph-type depending on \(\psi -\)Riemann–Liouville fractional integral operator associated with periodic-type fractional integral boundary conditions in a weighted space of continuous functions. We shall prove the existence and unique...
Article
Full-text available
In this manuscript we introduce the notion of (α,β,ψ,ϕ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\alpha,\beta,\psi,\phi)$\end{document}-interpolative contraction...
Article
Full-text available
Following publication of the original article [1], one of the corresponding author’s email was found to be incorrect. The correct emails of the corresponding author should be: [email protected]; [email protected] The original paper has been updated.
Article
Full-text available
Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy...
Article
This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fix...
Article
Full-text available
In this paper, we introduce the notions of interpolative(φ,ψ)-type Z-contraction with respect to simulation function and quasi triangularθ-orbital admissible map-ping. Using these notions, some fixed point theorems are also established in the framework of metric space. An illustrative example is furnished to show that there exists a quasi triangula...
Article
In this short note, we propose a fixed point theorem in the setting of a Banach space without using a Picard operator.
Article
Full-text available
This article proposes four distinct kinds of symmetric contraction in the framework of complete F-metric spaces. We examine the condition to guarantee the existence and uniqueness of a fixed point for these contractions. As an application, we look for the solutions to fractional boundary value problems involving a generalized fractional derivative...
Article
Full-text available
In this paper, we consider some nonlinear contraction for set-valued operators and prove some fixed point results in the case of set-valued operators are ordered-close and not ordered-close, and in the case of set-valued operators are UCAV (LCAV) in quasi-ordered P M-spaces. Moreover, we present two examples and an application to show the validity...
Article
Let (M,d) be a metric space, X\subset M be a nonempty closed subset and K\subset M be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator F:X\to P(X) is said to be a strong Frum-Ketkov type operator if there exists \alpha\in ]0,1[ such that e_d(F(x),K)\le \alpha D_d(x,K), for every x\in X, where e_d is the excess...
Article
Full-text available
This manuscript deals with a class of Katugampola implicit fractional differential equations in -metric spaces. The results are based on the -Geraghty type contraction and the fixed point theory. We express an illustrative example. 1. Introduction and Preliminaries An interesting extension and unification of fractional derivatives of the type Capu...
Article
Full-text available
We deal with some impulsive Caputo-Fabrizio fractional differential equations in b b -metric spaces. We make use of α - ϕ \alpha \text{-}\phi -Geraghty-type contraction. An illustrative example is the subject of the last section.
Preprint
Full-text available
Taking into account that Rold\'an et al.'s ample spectrum contractions have managed to extend and unify more than ten distinct families of contractive mappings in the setting of metric spaces, in this manuscript we present a first study on how such concept can be implemented in the more general framework of fuzzy metric spaces in the sense of Kramo...
Article
Full-text available
In this paper, we investigate sufficient conditions for the existence of solutions to the system Tx=x,αi(x)=0E,i=1,2,…,r,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$...
Article
Full-text available
In this paper, we give a new coincidence point theorem for two operators on Hilbert spaces for certain operators by using the weak Ekeland variational principle. Our paper extends and improves the results on the topic in the literature. We consider a boundary value problem as an application of our results.
Article
Full-text available
This paper is aimed at presenting some coincidence point results using admissible mapping in the framework of the partial -metric spaces. Observed results of the article cover a number of existing works on the topic of “investigation of nonunique fixed points.” We express an example to indicate the validity of the observed outcomes. 1. Introductio...
Article
Full-text available
In this article, we introduce the notions of a soft inf -comparable contraction and soft comparable Meir-Keeler contraction in a soft metric space. Furthermore, we prove two soft fixed point theorems which assure the existence of soft fixed points for these two types of comparable contractions. The obtained results not only generalize but also unif...
Article
Full-text available
In this paper, we introduce a new sequential space as a generalization of M−metric spaces and M_b−metric spaces. In this generalized space we define two contractive mappings namely m−contraction and m−quasi contraction and prove some fixed point theorems for such type of mappings. Several illustrative examples have been presented in strengthening t...
Article
Full-text available
In this paper, we propose a notion of the Górnicki-Proinov type contraction. Then, we prove the uniqueness and existence of the fixed point for such mappings in the framework of the complete metric spaces. Some illustrative examples are also expressed to strengthen the observed results. 1. Introduction and Preliminaries The history of the fixed po...
Article
Full-text available
In this paper, we introduce a new class of compatible mappings, called S τ-compatible mappings and prove some related common fixed point theorems for six mappings involving the notion of'inverse C-class functions in the framework of b-metric spaces. We also present some corollaries that are indeed with shorter proofs and are improved form of some r...
Article
Full-text available
In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by...
Chapter
In this manuscript, we shall discuss fixed point results with a contractive iterative at a point in the setting of various abstract space. The first aim of this paper is to collect the corresponding basic results on the topic in the literature. After then, our purpose is to combine and connect several existing results in this direction by generaliz...
Article
Full-text available
In this paper, we first introduce a new class of the pointwise cyclic-noncyclic proximal contraction pairs. Then we consider the coincidence quasi-best proximity point problem for this class. Finally, we study the coincidence quasi-best proximity points of weak cyclic-noncyclic Kannan contraction pairs. We consider an example to indicate the validi...
Chapter
In this chapter, we consider the distinct hybrid type contractions in various abstract spaces. In this work, hybrid contraction refers to combination of not only linear and nonlinear contractions, but also interpolative contractions. The main goal of the chapter is to clarify the metric fixed point theory literature by using the hybrid type contrac...
Article
In this manuscript, we aim at investigating the existence of a fixed point theorem for the mappings that satisfy hybrid contraction in the setting of quasi-metric spaces. We provide examples to indicate the validity of the observed results.
Article
Full-text available
In this manuscript we investigate the existence of start-points for the generalized weakly contractive multi-valued mappings in the setting of left K-complete quasi-pseudo metric space. We provide an example to support the given result.
Article
Full-text available
In this manuscript we investigate the existence of start-points for the generalized weakly contractive multi-valued mappings in the setting of left K-complete quasi-pseudo metric space. We provide an example to support the given result.
Article
Full-text available
The main aim of this paper is to prove the existence of the fixed point of the sum of two operators in setting of the cone-normed spaces with the values of cone-norm belonging to an ordered locally convex space. We apply this result to prove the existence of global solution of the Cauchy problem with perturbation of the form (x?(t) = f[t,x(t)] + g[...
Article
Full-text available
In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ-Hilfer fractional differential equations. For our purpose, we use the α−ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \us...
Article
Full-text available
In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We...
Article
Full-text available
The aim of this paper is to establish some fixed point results for surrounding quasi-contractions in non-triangular metric spaces. Also, we prove the Banach principle of contraction in non-triangular metric spaces. As applications of our theorems, we deduce certain well-known results in b-metric spaces as corollaries.
Article
Full-text available
In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sou...
Article
Full-text available
In this paper, we introduce the notion of an α–ζ̃–[InlineEquation not available: see fulltext.]–Pata contraction that combines well-known concepts, such as the Pata contraction, the E-contraction and the simulation function. Existence and uniqueness of a fixed point of such mappings are investigated in the setting of a complete metric space. An exa...
Article
Full-text available
We introduce the notion of pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. We study the best proximity point problem for this class of mappings. We also study the same problem for the class of pointwise noncyclic-noncyclic relatively nonexpansive pairs involving orbits. Finally, under the assumption of weak proximal norma...
Article
Full-text available
In this paper, we present a result of stability, data Dependency and errors estimation for D Iteration Method. We also prove that errors in D iterative process is controllable. Especially stability, data dependence, controllability, error accumulation of such iterative methods are being studied.
Chapter
In this note, we aim to emphasize the significance of the nonunique fixed point results in an abstract space: partial metric space. Indeed, partial metric is a natural extension of the standard metric from the aspect of computer science. The presented results aim to cover and unify several results on the topic in the related literature. We also ind...
Article
In this manuscript, we introduce the notion of admissible hybrid Geraghty contraction and we investigate the existence of fixed points of such mappings in the setting of complete metric spaces. Our results not only extend and generalize several results in the fixed point theory literature, but also unify most of them. We give some corollaries to il...
Article
Full-text available
We prove the best proximity point results for condensing operators on C-class of functions, by using a concept of measure of noncompactness. The results are applied to show the existence of a solution for certain integral equations. We express also an illsutrative examples to indicate the validity of the observed results. MSC: 47H08; 54H25
Article
Full-text available
In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion about continuity with respect to the fractional derivative order. We find the answer to the question: When the fractional order...
Article
Full-text available
In this paper we consider a kind of Geraghty contractions by using mw-distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained.
Article
Full-text available
The goal of this work is to introduce the concept of -hybrid Wardowski contractions. We also prove related fixed-point results. Moreover, some illustrated examples are given. 1. Introduction Let represent the collection of functions so that(i) is strictly increasing(ii) for each sequence in , iff (iii) there is so that Definition 1 (see [1]). A ma...
Article
Full-text available
In this note, we aim to review the recent results on F-contractions, introduced by Wardowski. After examining the fixed point results for such operators, we collect the sequent results in this direction in a different setting. One of the aims of this survey is to provide a complete collection of several fixed generalizations and extensions of F-con...
Article
Full-text available
In this paper, we investigate the existence of a unique coupled fixed point for α−admissible mapping which is of Fψ1,ψ2−contraction in the context of M−metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient condit...
Article
The purpose of this paper is to present some fixed point results in ε−chainable complete b−metric spaces that are inspired from famous result of Edelstein, published in 1961.
Article
Full-text available
Abstract This research intends to investigate the existence results for both coincidence points and common fixed point of generalized Geraghty multi-valued mappings endowed with a directed graph. The proven results are supported by an example. We also consider fractional integral equations as an application.
Article
Full-text available
In this paper we investigate the existence and uniqueness of fixed points of certain \((\phi ,F)\)-type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular examp...
Article
The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2<α ≤ 3 is studied. The BVP is transformed into an integral equation and discussed by means of a fixed point problem for an integral operator. Conditions for the existence and uniqueness of a fixed poi...
Article
Full-text available
The main goal of the present paper is to obtain several fixed point theorems in the framework of -quasi-metric spaces, which is an extension of -metric spaces. Also, a Hausdorff -distance in these spaces is introduced, and a coincidence point theorem regarding this distance is proved. We also present some examples for the validity of the given resu...
Article
Full-text available
In this paper, we have established some fixed-point results for the class of multivalued -contractions in the setting of extended -metric space. An example is furnished to show the validity of our results. The results we have obtained generalize/extend many recent results by Asl, Bota, Samreen et al., and those contained therein. 1. Introduction a...
Article
Full-text available
In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0 ) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-met...
Article
In this paper, we introduce a new contraction, namely, almost {\mathcal{Z}} contraction with respect to \zeta \in {\mathcal{Z}} , in the setting of complete metric spaces. We proved that such contraction possesses a fixed point and the given theorem covers several existing results in the literature. We consider an example to illustrate our result.
Article
Full-text available
In this paper, we introduce some common fixed point theorems for two distinct self-mappings in the setting of metric spaces by using the notion of a simulation function introduced in 2015. The contractivity conditions have not to be verified for all pairs of points of the space because it is endowed with an antecedent conditions. They are also of r...
Article
Full-text available
In this manuscript, we will investigate the existence of fixed points for mappings that satisfy some hybrid type contraction conditions in the setting of quasi-metric spaces. We provide examples to assure the validity of the given results. The results of this paper generalize several known theorems in the recent literature.
Article
Full-text available
In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results of the paper cover several existing results in the literature.
Article
Full-text available
In this paper, we consider a new distance structure, extended Branciari b-distance, to combine and unify several distance notions and obtain fixed point results that cover several existing ones in the corresponding literature. As an application of our obtained result, we present a solution for a fourth-order differential equation boundary value pro...
Article
In this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.
Article
Full-text available
In this paper, we give a proof of a fixed point theorem of Ćirić in b-metric spaces. Our result is supported with a suitable example. As a corollary of our results, we obtain a well known fixed point theorem in b-metric spaces.
Article
Full-text available
In this manuscript, we introduce two notions, Pata–Suzuki Z -contraction and Pata Z -contraction for the pair of self-mapping g , f in the context of metric spaces. For such types of contractions, both the existence and uniqueness of a common fixed point are examined. We provide examples to illustrate the validity of the given results. Further, we...