Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 4Existence and Uniqueness of Solutions for a Nabla Fractional Boundary Value Problem With Discrete Mittag{leffler Kernel(inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2021) Jonnalagadda, Jagan Mohan; Baleanu, Dumitru; Baleanu, Dumitru; MatematikWe consider a two-point boundary-value problem of order 1 < alpha < 3/2 involving nabla fractional differences with discrete Mittag-Leffler kernels. In [2], the authors obtained an expression for the Green's function of this boundary value problem. We determine an upper bound for the Green's function and derive a Lyapunov-type inequality. Further, we also establish sufficient conditions on existence and uniqueness of solutions for the corresponding nonlinear problem using fixed point theorems.Article Citation - Scopus: 11An Open Discussion: Interpolative Metric Spaces(DergiPark, 2023) Karapınar, E.The main goal of this paper is to introduce a new abstract structure (so called, interpolative metric space) as a generalization of a standard metric space. We shall consider the analog of Banach Mapping Principle in the context of this new structure. © 2023, DergiPark. All rights reserved.Article The Hausdorff-Pompeiu Distance in Gn-Menger Fractal Spaces(Mdpi, 2022) Saadati, Reza; Li, Chenkuan; Jarad, Fahd; O'Regan, Donal; O’Regan, DonalThis paper introduces a complete Gn-Menger space and defines the Hausdorff-Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for Gn-Menger-theta-contractions in fractal spaces.Article Citation - WoS: 9Citation - Scopus: 13Extended Proinov X-Contractions in Metric Spaces and Fuzzy Metric Spaces Satisfying the Property Nc by Avoiding the Monotone Condition(Springer-verlag Italia Srl, 2022) Martinez-Moreno, Juan; Shahzad, Naseer; Roldan Lopez de Hierro, Antonio Francisco; Karapinar, ErdalIn 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 conditions involving auxiliary functions whose role is increasingly decisive, and which are acquiring a prominent role in Functional Analysis. Very recently, Proinov introduced new fixed point results that have very much attracted the researchers' attention especially due to the extraordinarily weak conditions on the auxiliary functions considered. However, one of them, the nondecreasing character of the main function, has been used for many years without the chance of being replaced by another alternative property. In this way, several researchers have recently raised this question as an open problem in this field of study. In order to face this open problem, in this work we introduce a novel class of auxiliary functions that serve to define contractions, both in metric spaces and in fuzzy metric spaces, which, in addition to generalizing to Proinov contractions, avoid the nondecreasing character of themain auxiliary function. Furthermore, we present these new results in the setting of fuzzy metric spaces that satisfy the conditionNC, which open new possibilities in the metric theory compared to classic non-Archimedean fuzzy metric spaces. Finally, we include some illustrative examples to show how to apply the novel theorems to cases that are not covered by other previous results.Article Citation - WoS: 14Citation - Scopus: 17Interpolative Meir-Keeler Mappings in Modular Metric Spaces(Mdpi, 2022) Fulga, Andreea; Yesilkaya, Seher Sultan; Karapinar, ErdalModular 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 types via admissible mappings for fixed point theory. Our results bring together several results available in the current corresponding literature.Article Citation - Scopus: 45Interpolative Kannan-Meir Type Contraction(DergiPark, 2021) Karapınar, E.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. © 2021, DergiPark. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 13Contraction in Rational Forms in the Framework of Super Metric Spaces(Mdpi, 2022) Karapinar, Erdal; Fulga, AndreeaIn 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 Citation - WoS: 22Citation - Scopus: 30Global Stability Results for Volterra-Hadamard Random Partial Fractional Integral Equations(Springer-verlag Italia Srl, 2023) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Salim, AbdelkrimThis paper investigates the existence and stability of random solutions of a class of Hadamard fractional order functional partial integral equations with random effects in Banach spaces.Article Citation - WoS: 144Citation - Scopus: 156Uniqueness 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, RezanThis 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.Article Citation - WoS: 26Citation - Scopus: 30Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces(Mdpi, 2021) Fulga, Andreea; Karapinar, Erdal; Shahzad, Naseer; Roldan Lopez de Hierro, Antonio FranciscoVery 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 metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.