2008•Numerical Functional Analysis and OptimizationRequires access

Block Iterative Methods for a Finite Family of Generalized Nonexpansive Mappings in Banach Spaces

Takanori Ibaraki, Wataru Takahashi

Abstract

In this paper, we study an operator generated by a finite family of generalized nonexpansive mappings in a Banach space. We first prove that the set of fixed points of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate a common fixed point of the family of generalized nonexpansive mappings. We finally apply our results to solve the feasibility problem in Banach spaces.

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Key concepts: Mathematics, Banach space, Fixed point, Sequence (biology), Operator (biology), Block (permutation group theory), Set (abstract data type), Iterative method