Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 1998; 35(4): 933-944

Printed December 1, 1998

Copyright © The Korean Mathematical Society.

A new minimum theorem and its applications

Won Kyu Kim, Dong Il Rim, and Sung Mo Im

Chungbuk National University, Chungbuk National University and Chungbuk National University

Abstract

In this paper we first prove a new minimum theorem using the upper semicontinuity of minimizing functions, which is comparable to Berge's theorem. Next, as applications, we shall prove the existence of equilibrium in generalized games and the existence theorem of zeros.

Keywords: minimum theorem, generalized game, equilibrium,\break strong topology, fixed point

MSC numbers: Primary 90A15, 52A07; Secondary 59J50