Browsing by Author "De la Sen, M."

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Citation - WoS: 10
Citation - Scopus: 12
Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications To Impulsive Differential and Difference Equations
(Hindawi Ltd, 2013) De la Sen, M.; Karapinar, E.
This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.
Citation - WoS: 21
Citation - Scopus: 18
On a Cyclic Jungck Modified ts-iterative Procedure With Application Examples
(Elsevier Science inc, 2014) De la Sen, M.; Karapinar, E.; Alemdaroğlu Temel, Mine; Alemdaroğlu Temel, Mine
This article investigates some convergence properties of quasi-cyclic and cyclic Jungck modified TS-iterative schemes in complete metric spaces and Banach spaces. The uniqueness of the best proximity points is investigated. It is basically assumed that one of the self-mappings is asymptotically nonexpansive while the other is asymptotically contractive with several particular cases. Some application examples are also discussed. (C) 2014 Elsevier Inc. All rights reserved.