Browsing by Author "Karapinar, E."

Now showing 1 - 13 of 13

Citation - WoS: 22
Citation - Scopus: 32
A solution of the fractional differential equations in the setting of b-metric space
(Vasyl Stefanyk Precarpathian Natl Univ, 2021) Afshari, H.; Karapinar, E.; 19184; Matematik
In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems {D(c)(mu)w(sigma) +/- D(c)(nu)w(sigma) = h(sigma, w(sigma)), sigma is an element of J, 0 < nu < mu < 1, w(0) = w(0), where D-mu, D-nu is the Caputo derivative of order mu, nu, respectively and h: J x R -> R is continuous. The results are well demonstrated with the aid of exciting examples.
Citation - Scopus: 4
Cirić And Meir-Keeler Fixed Point Results In Super Metric Spaces
(Biemdas Academic Publishers, 2022) Agarwal, R.P.; Karapinar, E.; Khojasteh, F.; 19184; Matematik
In this paper, we consider Meir Keeler and Ćirić contractions in the setting of super metric spaces which is an interesting generalization of standard metric space. We investigate the existence and uniqueness of fixed points for these operators in this new structure. ©2022 Applied Set-Valued Analysis and Optimization.
Citation - WoS: 197
Citation - Scopus: 192
Existence and uniqueness of a common fixed point on partial metric spaces
(Pergamon-elsevier Science Ltd, 2011) Abdeljawad, T.; Karapinar, E.; Tas, K.; 19184; 4971; Matematik
In this work, a general form of the weak phi-contraction is considered on partial metric spaces, to get a common fixed point. It is shown that self-mappings S, T on a complete partial metric space X have a common fixed point if it is a generalized weak phi-contraction. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 10
Citation - Scopus: 9
FIXED POINT RESULTS IN epsilon-CHAINABLE COMPLETE b-METRIC SPACES
(House Book Science-casa Cartii Stiinta, 2020) Chifu, C.; Karapinar, E.; Petrusel, G.; 19184; Matematik
The purpose of this paper is to present some fixed point results in epsilon-chainable complete b-metric spaces that are inspired from famous result of Edelstein, published in 1961.
Citation - WoS: 11
Citation - Scopus: 12
Mann and Ishikawa Iterative Processes for Cyclic Relatively Nonexpansive Mappings in Uniformly Convex Banach Spaces
(Yokohama Publications, 2021) Aliyari, M.; Gabeleh, M.; Karapinar, E.; Matematik
In this manuscript, we study the convergence of best proximity points for cyclic relatively nonexpansive mappings in the setting of uniformly convex Banach spaces by using a projection operator defined on proximal pairs. To this end, we consider the Mann and Ishikawa iteration schemes and obtain strong convergence results for cyclic relatively nonexpansive mappings. A nu¬merical example is presented to support the main result. We then discuss on noncyclic version of relatively nonexpansive mappings in order to study some convergence conclusions in both uniformly convex Banach spaces and Hilbert spaces. © 2021 Yokohama Publications. All rights reserved.
On the New Trends Regarding Nonlinear Contractions
(Springer Science and Business Media Deutschland GmbH, 2025) Karapinar, E.; Cvetković, M.
The concept of nonlinear contractions is studied by the researchers in the area of Metric Fixed Point Theory more than a half of the century, but during the last decade we are witnessing tremendous interest in the new approach in the area of nonlinear contractions, the concept of F-contraction. This idea has been broadly investigated and there are numerous results regarding modifications of F-contraction and its generalizations in various settings. We will collect several modifications, comment on their mutual relation along with their relation with some other types of nonlinear contractions, and discuss some new result regarding its generalizations. Also, we will present some applications of those fixed point theorems and compare them with previous results regarding those problems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
Citation - Scopus: 1
Perov-type results for multivalued mappings
(World Scientific Publishing Co. Pte. Ltd., 2023) Cvetković, M.; Karapinar, E.; Rakočevié, V.; Yeşilkaya, S.S.; 19184; Matematik
Inspired by the results of Russian mathematician A. I. Perov from the 1960s, several authors have studied and extended these results by generalizing the contractive condition or changing the setting. In this chapter, we will present and analyze Perov-type results regarding multivalued operators and related applications. © 2023 World Scientific Publishing Company. All rights reserved.
Qualitative Analysis of Nonlinear Hilfer Fractional Implicit Differential Equations in a Banach Space
(DergiPark, 2023) Dhawan, K.; Vats, R.K.; Karapinar, E.; Matematik
This article focuses on the class of nonlinear implicit Hilfer-type fractional differential equations. By using the non-linear growth condition, we have derived the existence of at least one solution by applying Schauder’s fixed point theorem and using Lipschitz conditions, we have derived the uniqueness of the solution with the help of the Banach contraction principle. In addition, we have discussed the stability analysis by using Ulam-Hyers and Ulam-Hyers-Rassias stabilities. All results of this paper are established in a Banach space instead of R. We illustrate our results with the help of two examples. © 2023, DergiPark. All rights reserved.
Citation - WoS: 11
Citation - Scopus: 10
Recent Advances On Metric Fixed Point Theory: A Review
(Ministry Communications & High Technologies Republic Azerbaijan, 2023) Karapinar, E.; 19184; Matematik
In this note, we underline that some of the recent metric fixed point results overlap or repeat the previously existing corresponding ones. Further, we observe that some recently published results, which we might perceive as a generalization from the first point of view, are in fact equivalent. For the clarification and clearing of the literature, this review paper claims to play a crucial role.
Citation - Scopus: 3
Revisiting Fixed Point Results with a Contractive Iterative at a Point
(Springer Science and Business Media Deutschland GmbH, 2021) Karapinar, E.; 19184; Matematik
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 generalizing the famous theorem of Matkowski. We shall consider some consequence of our main result to illustrate its genuineness. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - WoS: 1
Citation - Scopus: 1
SOLVING EXISTENCE PROBLEMS VIA F-CONTRACTION IN MODIFIED b-METRIC SPACES
(Turkic World Mathematical Soc, 2022) Karapinar, E.; Sedghi, S.; Shobe, N.; 19184; Matematik
In this paper, we introduce a new abstract structure, expanded b-metric, as an natural extension of b-metric. We also define basic topological notions in expanded b -metric to able to investigate the existence of fixed point for such mappings under various F-contractive conditions. We provide example to illustrate the results presented herein.
Citation - WoS: 12
Citation - Scopus: 12
Solving Integral Equations by Means of Fixed Point Theory
(Wiley, 2022) Karapinar, E.; Fulga, A.; Shahzad, N.; Roldan Lopez de Hierro, A. F.; 19184; Matematik
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 or multiple. One of the recent methodologies that is having great success in this field of study is the fixed point theory. Its iterative procedures are applicable to a great variety of contexts in which other algorithms fail. In this paper, we study a very general class of integral equations by means of a novel family of contractions in the setting of metric spaces. The main advantage of this family is the fact that its general contractivity condition can be particularized in a wide range of ways, depending on many parameters. Furthermore, such a contractivity condition involves many distinct terms that can be either adding or multiplying between them. In addition to this, the main contractivity condition makes use of the self-composition of the operator, whose associated theorems used to be more general than the corresponding ones by only using such mapping. In this setting, we demonstrate some fixed point theorems that guarantee the existence and, in some cases, the uniqueness, of fixed points that can be interpreted as solutions of the mentioned integral equations.
Citation - WoS: 8
Citation - Scopus: 10
Study of Γ−simulation functions, zΓ−contractions and revisiting the l −contractions
(Univ Nis, Fac Sci Math, 2021) Karapinar, E.; Joonaghany, Gh Heidary; Khojasteh, E.; Radenovic, S.; 19184; Matematik
In this paper, we introduce the notions of Z(Gamma)-contractions and Suzuki Z(Gamma)-contractions via Gamma-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(Gamma)-contraction. In addition, some notable examples are given to illustrate and support the obtained results.