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Article Citation - WoS: 1Relationships Between Tropical Eigenvectors and Tropical Fixed Points of the Group gl(2, R)(Forum Editrice Univ Udinese, 2020) Hayat, Umar; Farid, Ghulam; Karapinar, Erdal; MathematicsThe eigenvalues, eigenvectors and fixed points of matrices have many applications in various branches of science and many mathematical disciplines. In this paper first we introduce the concept of tropical fixed points, then we calculate the tropical eigenvalues and tropical eigenvectors of GL(2, R). Furthermore we give relationships between tropical eigenvectors and tropical fixed points of GL(2, R).Article Existence, Uniqueness and Successive Approximations for (λ, Ψ)-Hilfer Fractional Differential Equations(Univ Politehnica Bucharest, Sci Bull, 2024) Krim, Salim; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, ErdalThe focus of this paper is on investigating a particular type of nonlinear (lambda, psi)-Hilfer fractional differential equations, and analyzing their existence results. Our approach involves utilizing Banach's fixed point theorem, and we also explore the global convergence of successive approximations to provide additional insights into the topic. To further illustrate our findings, we provide some examples that supplement our main results.Article Mild Solutions for Neutral Conformable Fractional Order Functional Evolution Equations Using Meir-Keeler Type Fixed Point Theorem(University Politehnica Bucharest, Sci Bull, 2025) Berrighi, Fatma; Medjadj, Imene; Karapinar, ErdalOur mission is to demonstrate the existence, uniqueness, attractiveness, and controllability of mild solutions to neutral conformable fractional-order functional evolution equations, specifically of order between 1 and 2. These intriguing equations encompass finite delay, all while adhering to local conditions within a separable Banach space. By invoking Meir-Keeler's fixed-point Theorem and enhancing it with measures of noncompactness, we establish the existence of these solutions. To highlight the potency of our approach, we present a captivating example.Article Citation - WoS: 41Citation - Scopus: 44Some New Fixed Point Theorems in Fuzzy Metric Spaces(Ios Press, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Manro, SaurabhThe aim of this paper is to introduce a new class of contractive mappings such as fuzzy alpha-psi-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results.Article Citation - WoS: 3On Ciric Type φ-Geraghty Contractions(Chiang Mai Univ, Fac Science, 2019) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper we introduce the notions of phi-Geraghty contractions and Ciric type phi-Geraghty contractions. We also investigate under which conditions such mappings posses a unique fixed point in the framework of complete metric spaces. We consider examples to show the validity of our main results.Article Citation - WoS: 1Rational Contractive Mappings of Integral Type on b-metric Spaces(Univ Prishtines, 2017) Alsulami, Hamed H.; Karapinar, Erdal; Piri, Hossien; Rahrovi, Samira; Zarghami, RamazanThe aim of this paper is to introduce (alpha, psi)- rational contractive mappings of integral type and analyze the existence of fixed points for these mappings in b-metric spaces. Our results extend the results in Karapinar et al. [35] and well known fixed point theorems in the literature.Article Citation - WoS: 5AN IMPLICIT RELATION FOR MEIR-KEELER TYPE MAPPINGS ON METRIC-LIKE SPACES(Univ Prishtines, 2017) Aydi, Hassen; Felhi, Abdelbasset; Karapinar, Erdal; Alshaikh, H. AliIn this note, we introduce an implicit relation for Meir-Keeler type mappings via auxiliary pair of functions (alpha,psi) in the context of metric-like spaces. We investigate the existence and uniqueness of a common fixed point of such operators. The obtained results extend, improve and unify several existing fixed point results in the literature.Article Citation - WoS: 28Fixed Points on Quasi-Metric Spaces Via Simulation Functions and Consequences(Univ Prishtines, 2018) Aydi, Hassen; Felhi, Abdelbasset; Karapinar, Erdal; Alojail, Fatimah A.In this paper, we provide some fixed points for triangular alpha-admissible contraction mappings via simulations functions in the class of quasimetric spaces. Some consequences are presented. We also give some illustrated examples.Article Remark on p-d< Operator(Chiang Mai Univ, Fac Science, 2017) Gopal, Dhananjay; Karapinar, ErdalIn this short communication, we show that P-D, operator fall in the class of weakly compatible (respectively, occasionally weakly compatible) in the presence of a unique common fixed point (respectively, multiple common fixed points) of the given maps.Article Citation - WoS: 5Citation - Scopus: 7On Jaggi Type Contraction Mappings(Univ Politehnica Bucharest, Sci Bull, 2018) Karapinar, Erdal; MathematicsBy a work of Jaggi, it is known that the existence of certain inequalities for continuous maps over metric spaces implies the existence and uniqueness of fixed points. In this paper, we show that if p denotes a partial metric, the existence of a rational form of type p(Tt,Ts) <= a(1) p(t,Tt).p(s,Ts)/d(t,s)+a(2)p(t,s) for some a 1 and a 2 with a(1) + a(2) < 1 for a continuous map T over a partial metric space leads to the same conclusions, that is, the existence and uniqueness of fixed points.
