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Generalized KKM-type theorems for best proximity points

Hoonjoo Kim
대한수학회 (The Korean Mathematical Society)|2016.09|대한수학회보 (Bulletin of the KMS)|제53권 제5호|pp. 1363-1371

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참고문헌

키워드

admissiblebest proximity pointbest proximity pairgeneralized KKM$R$-KKMunionly openquasi-lower semicontinuoushyperconvex
주제분류수학

초록

This paper is concerned with best proximity points for multimaps in normed spaces and in hyperconvex metric spaces. Using the generalized KKM theorem, we deduce new best proximity pair theorems for a family of multimaps with unionly open fibers in normed spaces. And we prove a new best proximity point theorem for quasi-lower semicontinuous multimaps in hyperconvex metric spaces.

Abstract

This paper is concerned with best proximity points for multimaps in normed spaces and in hyperconvex metric spaces. Using the generalized KKM theorem, we deduce new best proximity pair theorems for a family of multimaps with unionly open fibers in normed spaces. And we prove a new best proximity point theorem for quasi-lower semicontinuous multimaps in hyperconvex metric spaces.

참고문헌 (15)

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