Browsing by Author "Erhan, Inci M."

Now showing 1 - 6 of 6

Citation - WoS: 52
Citation - Scopus: 59
F-Contraction Mappings on Metric-Like Spaces in Connection With Integral Equations on Time Scales
(Springer-verlag Italia Srl, 2020) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Agarwal, Ravi P.
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 example which demonstrates our theoretical results.
Citation - WoS: 1
Citation - Scopus: 4
Fixed Point Theorems for Mappings With a Contractive Iterate at a Point in Modular Metric Spaces
(House Book Science-casa Cartii Stiinta, 2022) Karapinar, Erdal; Aksoy, Umit; Fulga, Andreea; Erhan, Inci M.
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.
Citation - WoS: 3
Citation - Scopus: 3
On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation
(Taylor & Francis Ltd, 2021) Erhan, Inci M.; Fulga, Andreea; Karapinar, Erdal; Aksoy, Umit
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.
Citation - WoS: 198
Citation - Scopus: 168
On the Solution of a Boundary Value Problem Associated With a Fractional Differential Equation
(Wiley, 2024) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Adiguzel, Rezan Sevinik
The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2 < alpha <= 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 point for the integral operator are derived via b-comparison functions on complete b-metric spaces. In addition, estimates for the convergence of the Picard iteration sequence are given. An estimate for the Green's function related with the problem is provided and employed in the proof of the existence and uniqueness theorem for the solution of the given problem. Illustrative examples are presented to support the theoretical results.
Citation - WoS: 146
Citation - Scopus: 157
On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions
(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Karapınar, Erdal; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Matematik
The aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.
Citation - WoS: 143
Citation - Scopus: 145
Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions
(Springer-verlag Italia Srl, 2021) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Sevinik-Adiguzel, Rezan
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 fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.