Browsing by Author "Karapinar, Erdal"

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A Brief Overview and Survey of the Scientific Work by Feng Qi
(2022) Agarwal, Ravi Prakash; Karapinar, Erdal; Kostić, Marko; Cao, Jian; Du, Wei-Shih; 19184
In the paper, the authors present a brief overview and survey of the scientific work by Chinese mathematician Feng Qi and his coauthors.
A common fixed point theorem of a Greguš type on convex cone metric spaces
(2011) Abdeljawad, Thabet; Karapinar, Erdal; 19184
The result of Ćirić [1] on a common fixed point theorem of Greguš type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral.
A generalized contraction principle with control functions on partial metric spaces
(Pergamon-elsevier Science Ltd, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Karapınar, Erdal; Karapinar, Erdal; Tas, Kenan; Taş, Kenan; 19184; 4971
Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.
A Note on the Gornicki-Proinov Type Contraction
(2021) Karapinar, Erdal; De La Sen, Manuel; Fulga, Andreea; 19184
In this paper, we propose a notion of the Gornicki-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.
Applying new fixed point theorems on fractional and ordinary differential equations
(Springer, 2019) Karapınar, Erdal; Karapinar, Erdal; Abdeljawad, Thabet; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; 234808
In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary value problems and fractional boundary value problems with integral type boundary conditions in the frame of some Caputo type fractional operators.
Contraction in Rational Forms in the Framework of Super Metric Spaces
(2022) Karapinar, Erdal; Fulga, Andreea; 19184
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.
Controllability of Second Order Functional Random Differential Equations with Delay
(2022) Benchohra, Mouffak; Bouazzaoui, Fatima; Karapinar, Erdal; Salim, Abdelkrim; 19184
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. Finally, an example is given to validate the theory part.
Coupled fixed points for meir-keeler contractions in ordered partial metric spaces
(Hindawi Ltd, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Aydi, Hassen; Karapınar, Erdal; Karapinar, Erdal; 19184
In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F : X x X -> X and g : X -> X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012)
Fixed Point Theorem On Partial Metric Spaces Involving Rational Expressions
(Univ Miskolc inst Math, 2013) Karapınar, Erdal; Karapinar, Erdal; Shatanawi, Wasfi; Taş, Kenan; Tas, Kenan; 4971
We establish a fixed point theorem involving a rational expression in a complete partial metric space. Our result generalizes a well-known result in (usual) metric spaces. Also, we introduce an example to illustrate the usability of our result.
Fixed Point Theorems For Mappings With A Contractive Iterate At A Point In Modular Metric Spaces
(2022) Karapinar, Erdal; Aksoy, Ümit; Fulga, Andreea; Erhan, İnci M.; 19184
In this manuscript, we introduce two new types of contraction, namely, w-contraction and strong Sehgal w-contraction, in the framework of modular metric spaces. We indicate that under certain assumptions, such mappings possess a unique fixed point. For the sake of completeness, we consider examples and an application to matrix equations.
Fixed points for cyclic orbital generalized contractions on complete metric spaces
(de Gruyter Open Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Romaguera, Salvador; Taş, Kenan; Tas, Kenan; 4971
We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293-303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.
Generalized (C)-conditions and related fixed point theorems
(Pergamon-elsevier Science Ltd, 2011) Karapınar, Erdal; Karapinar, Erdal; Tas, Kenan; Taş, Kenan; 19184; 4971
In this manuscript, the notion of C-condition [K. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] is generalized. Some new fixed point theorems are obtained. (C) 2011 Elsevier Ltd. All rights reserved.
Generalized alpha-psi-contractive type mappings of integral type and related fixed point theorems
(Springer, 2014) Karapınar, Erdal; Karapinar, Erdal; Shahi, Priya; Taş, Kenan; Tas, Kenan; 19184; 4971
The aim of this paper is to introduce two classes of generalized alpha-psi-contractive type mappings of integral type and to analyze the existence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude of relevant fixed point theorems of the existing literature.
Neutral functional sequential differential equations with Caputo fractional derivative on time scales
(2022) Lazreg, Jamal Eddine; Benkhettou, Nadia; Benchohra, Mouffak; Karapinar, Erdal; 19184
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 applications, two examples are included to show the applicability of our results.
Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag–Leffler kernel
(Pergamon-elsevier Science Ltd, 2019) Jarad, Fahd; Alqahtani, Badr; Fulga, Andreea; Karapınar, Erdal; Jarad, Fahd; Karapinar, Erdal; 234808
In this manuscript, we aim to refine and characterize nonlinear F-contractions in a more general framework of b-metric spaces. We investigate the existence and uniqueness of such contractions in this setting. We discuss the solutions to differential equations in the setting of fractional derivatives involving Mittag-Leffler kernels (Atangana-Baleanu fractional derivative) by using nonlinear F-contractions that indicate the genuineness of the presented result. (C) 2019 Elsevier Ltd. All rights reserved.
On coupled fixed point theorems on partially ordered G-metric spaces
(Springeropen, 2012) Karapınar, Erdal; Karapinar, Erdal; Kaymakçalan, Billur; Kaymakcalan, Billur; Tas, Kenan; Taş, Kenan; 19184; 4971
In this manuscript, we extend, generalize and enrich some recent coupled fixed point theorems in the framework of partially ordered G-metric spaces in a way that is essentially more natural.
On Istrescu Type Contractions in b-Metric Spaces
(2020) Karapinar, Erdal; Fulga, Andreea; Petrusel, Adrian; 19184
In this paper, we introduce the notions of alpha-almost Istrtescu contraction of type E and of type E in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences.
On the boundary value problems of Hadamard fractional differential equations of variable order
(2023) Benkerrouche, Amar; Souid, Mohammed Said; Karapinar, Erdal; Hakem, Ali; 19184
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 constant functions. All results in this study are established using Krasnoselskii fixed-point theorem and the Banach contraction principle. Further, the Ulam–Hyers stability of the given problem is examined, and finally, we construct an example to illustrate the validity of the observed results.
Preface to the Special Issue “A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi”
(2023) Du, Wei-Shih; Agarwal, Ravi Prakash; Karapinar, Erdal; Kostić, Marko; Cao, Jian; 19184
Quadruple fixed point theorems for nonlinear contractions on partial metric spaces
(Univ Politecnica Valencia, Editorial Upv, 2014) Karapınar, Erdal; Karapinar, Erdal; Tas, Kenan; Taş, Kenan; 19184; 4971
The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapmar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.