Block Iterative Methods for a Finite Family of Generalized Nonexpansive Mappings in Banach Spaces |
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| Authors: | Takanori Ibaraki |
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| Institution: | Information and Communications Headquarters , Nagoya University , Nagoya, Aichi, Japan |
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| 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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| Keywords: | Banach space Block iterative method Feasibility problem Generalized nonexpansive mapping Image recovery Sunny generalized nonexpansive retract |
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