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.
Hoonjoo Kim
Sehan University
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
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