The general iterative methods for nonexpansive mappings in Banach spaces

Authors:
Rattanaporn Wangkeeree;Narin Petrot;Rabian Wangkeeree
Affiliations:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand 65000;Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand 65000;Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand 65000
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

In this paper, we introduce a general iterative approximation method for finding a common fixed point of a countable family of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. As applications, at the end of the paper, we apply our results to the problem of finding a zero of an accretive operator. The main result extends various results existing in the current literature.