Abstract
It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.
Highlights
Introduction and PreliminariesThroughout the paper, we assume that X is a real Banach space and C ⊂ X is a subset
It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space
We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points
Summary
Introduction and PreliminariesThroughout the paper, we assume that X is a real Banach space and C ⊂ X is a subset. It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces.
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