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Article ON A GENERALIZED α-ADMISSIBLE RATIONAL TYPE CONTRACTIVE MAPPING(Yokohama Publ, 2016) Erhan, Inci M.; Kir, MehmetRecently, many generalized contractive conditions which involve rational contractive inequalities have been introduced in the context of partially ordered metric spaces. In this paper, we aim to give a generalized rational contractive condition which involves some of these results without need of extra restrictions.Article Citation - WoS: 27ON α-ψ-GERAGHTY CONTRACTION TYPE MAPPINGS ON QUASI-BRANCIARI METRIC SPACES(Yokohama Publ, 2016) Karapinar, Erdal; Pitea, ArianaIn this paper, we state and prove results regarding alpha-psi-Geraghty contractive mappings in the setting of quasi-Branciari metric spaces. We provide existence and uniqueness results for periodic and fixed points of such mappings.Article Citation - WoS: 16Citation - Scopus: 19Fixed Point Theorems in Quasi-Metric Spaces and Applications To Multidimensional Fixed Point Theorems on g-metric Spaces(Yokohama Publ, 2015) Agarwal, Ravi; Karapinar, Erdal; Roldan-Lopez-De-Hierro, Antonio-Francisco; MathematicsIn this manuscript, we investigate the equivalence of the coupled fixed point theorems in quasi-metric spaces and in G-metric spaces. We also notice that coupled fixed point theorems in the setting of G-metric spaces can be derived from their corresponding versions in quasi-metric spaces. Our results generalize and unify several fixed point theorems in the context of G-metric spaces in the literature.Article Citation - WoS: 1DISCUSSION ON THE EQUIVALENCE OF W-DISTANCES WITH Ω-DISTANCES(Yokohama Publ, 2015) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, ErdalIn this manuscript, we study some relationships between w-distances on metric spaces and Omega-distances on G*-metric spaces. Concretely we show that the class of all w-distances on metric spaces is a subclass of all Omega-distances on G*-metric spaces. Then, researchers must be careful because some recent results about w-distances (for instances, in the topic of fixed point theory) can be seen as simple consequences of their corresponding results about Omega-distances. In this sense, we show how to translate some results between different metric models.Article Citation - WoS: 1EXISTENCE OF FIXED POINTS FOR NEW PRESIC TYPE MULTIVALUED OPERATORS(Yokohama Publ, 2017) Ali, Muhammad Usman; Kamran, Tayyab; Karapinar, ErdalIn this paper, we shall generalize the convergence theorem introduced by Presic in 1965, by introducing the notions of alpha-Presic type contractive multivalued operators. We shall also construct some examples to prove the generality of our results.Conference Object Citation - WoS: 2Citation - Scopus: 1Rational Forms That Imply the Uniqueness of Fixed Points in Partial Metric Spaces(Yokohama Publ, 2019) Karapinar, Erdal; MathematicsIn this paper, we investigate the existence and uniqueness of fixed points of Jaggi type contractions by using a simulation function in the framework of partial metric spaces. Our results improve, extend and unify several results on the topic in the literature.Article Citation - WoS: 2Uniqueness of Solution for Second Order Nonlinear q-difference Equations With Multi-Point and Integral Boundary Conditions(Yokohama Publ, 2022) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Sevinik Adıgüzel, Rezan; Mathematics; MathematicsThe existence and uniqueness of the solution for the boundary value problem associated with nonlinear second-order q-difference equation is discussed by Banach contraction mapping theorem on b-metric spaces. The problem is converted to an integral equation and investigated via a fixed point problem for an integral operator. Existence and uniqueness conditions for a fixed point of the integral operator are obtained. Moreover, an example is introduced to support the main results.Article Citation - WoS: 68FIXED POINTS OF GENERALIZED α-ADMISSIBLE CONTRACTIONS ON b-METRIC SPACES WITH AN APPLICATION TO BOUNDARY VALUE PROBLEMS(Yokohama Publ, 2016) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.A general class of alpha-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations.Article Citation - WoS: 4Citation - Scopus: 4Common Periodic Soft Points of the Asymptotic Sequences in Soft Metric Spaces(Yokohama Publ, 2017) Chen, Chi-Ming; Karapinar, Erdal; MathematicsThe purpose of this paper is to study the important properties of soft sets and soft metric spaces, and then we prove some theorems which assures the existence of common periodic soft points for the asymptotic sequences with respect to the soft Meir-Keeler type functions on a complete soft metric space. Our results generalize many recent fixed point results in the literature.Article On the Existence and Uniqueness of Solutions of Fractional Dynamic Equations On Time Scales(Yokohama Publ, 2022) Erhan, Inci M.The existence and uniqueness of solutions of Cauchy problem for a nonlinear Caputo fractional dynamic equation of arbitrary order alpha > 0 is studied. The problem is treated as a fixed point problem posed on a b-metric space. A numerical example is presented to support the theoretical results.
