A GENESIS OF GENERAL KKM THEOREMS FOR ABSTRACT CONVEX SPACES

Authors

  • SEHIE PARK The National Academy of Sciences, Republic of Korea, Seoul 137-044 and Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea

Keywords:

Abstract convex space, (partial) KKM principle, KKM space, Generalized (G-) convex space, Fixed point

Abstract

In a recent work of the author [42], we obtained three general KKMtype theorems for abstract convex spaces. In this review, we show that two of them can be stated for intersectionally closedvaluedKKM maps in the sense of Luc et al. [13]. Each of such KKM type theorems contains a large number of previously known particular forms. We recall some of them due to the author in order to give a short history on such theorems. Further comments on related works are given.

Additional Files

Published

12/21/2011

Issue

Vol. 2 No. 1 (2011): JNAO

Section

Research Articles

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Copyright (c) 2010 Journal of Nonlinear Analysis and Optimization: Theory & Applications

Creative Commons License

This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.