Block Iterative Methods for a Finite Family of Generalized Nonexpansive Mappings in Banach Spaces
Takanori Ibaraki, Wataru Takahashi · Numerical Functional Analysis and Optimization · 2008
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.