On Best Proximity Point Theorems and Fixed Point Theorems for -Cyclic Hybrid Self-Mappings in Banach Spaces | Zendy

Manuel De la Sen | Zendy

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On Best Proximity Point Theorems and Fixed Point Theorems for -Cyclic Hybrid Self-Mappings in Banach Spaces

Author(s) -

Manuel De la Sen

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/183174

Subject(s) - mathematics , iterated function , banach space , fixed point , differentiable function , regular polygon , class (philosophy) , monotonic function , bregman divergence , function (biology) , pure mathematics , convex function , mathematical analysis , discrete mathematics , geometry , computer science , artificial intelligence , evolutionary biology , biology

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent -hybrid -cyclic self-mappings relative to a Bregman distance , associated with a Gâteaux differentiable proper strictly convex function in a smooth Banach space, where the real functions and quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping. Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

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