Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(5): 1363-1371

Online first article September 13, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150640

Copyright © The Korean Mathematical Society.

Generalized KKM-type theorems for best proximity points

Hoonjoo Kim

Sehan University

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.

Keywords: best proximity point, best proximity pair, generalized KKM, $R$-KKM, unionly open, quasi-lower semicontinuous, hyperconvex, admissible

MSC numbers: Primary 47H10, 47H04