Abstract
In this paper, we discuss sufficient and necessary conditions for the existence of best proximity points for non-self-α-nonexpansive mappings in Banach spaces. We obtain convergence results under some assumptions, and we prove the existence of common best proximity points for a family of non-self-α-nonexpansive mappings.
Highlights
Let (X, d) be a metric space and A a nonempty subset of X
In [ ], Sankar Raj obtained the existence theorem of a best proximity point for weakly contractive mappings as follows
Theorem . [ ] Let X be a uniformly convex Banach space, let A be a nonempty, closed, and convex subset of X, and let T : A → A be an α-nonexpansive mapping for some real number α such that α
Summary
Let (X, d) be a metric space and A a nonempty subset of X. In [ ], Sankar Raj obtained the existence theorem of a best proximity point for weakly contractive mappings as follows. [ ] Let X be a uniformly convex Banach space, let A be a nonempty, closed, and convex subset of X, and let T : A → A be an α-nonexpansive mapping for some real number α such that α
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