Abstract
Abstract In this paper, the existence of a best proximity point for relatively u-continuous mappings is proved in geodesic metric spaces. As an application, we discuss the existence of common best proximity points for a family of not necessarily commuting relatively u-continuous mappings.
Highlights
1 Introduction Let A be a nonempty subset of a metric space (X, d) and T : A → X
We investigate the existence of common best proximity points for a family of not necessarily commuting relatively u-continuous mappings
The result follows from Theorem once we show that PA ◦ T : A → A is a continuous mapping, where PA : X → A is a metric projection operator
Summary
Let A be a nonempty subset of a metric space (X, d) and T : A → X. In [ ], Sankar Raj and Veeramani used a convergence theorem to prove the existence of best proximity points for relatively nonexpansive mappings in strictly convex Banach spaces. Theorem [ ] Let A, B be nonempty compact convex subsets of a strictly convex Banach space X and T : A ∪ B → A ∪ B be a relatively u-continuous mapping.
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