Journal of the
Korean Mathematical Society
JKMS

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

Article

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J. Korean Math. Soc. 2002; 39(4): 579-591

Printed July 1, 2002

Copyright © The Korean Mathematical Society.

Fixed point theory for multimaps in extension type spaces

Ravi P. Agarwal, Donal O'Regan, and Sehie Park

Florida Institute of Technology, National University of Ireland, Seoul National University

Abstract

New fixed point results for the $\mathfrak A_c^\kappa\,$ selfmaps are given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.

Keywords: admissible class of multimaps, (approximate) extension space, Schauder admissible set, essential map, quasi-variational inequality

MSC numbers: 47H10, 54C60, 54H25, 55M20