Table of Contents
Journal of Operators
Volume 2013, Article ID 124962, 10 pages
http://dx.doi.org/10.1155/2013/124962
Research Article

Evolution of the Minimax Inequality of Ky Fan

1The National Academy of Sciences, ROK, Seoul 137-044, Republic of Korea
2Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea

Received 14 November 2012; Accepted 27 February 2013

Academic Editor: Ram U. Verma

Copyright © 2013 Sehie Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

There are quite a few generalizations or applications of the 1984 minimax inequality of Ky Fan compared with his original 1972 minimax inequality. In a certain sense, the relationship between the 1984 inequality and several hundreds of known generalizations of the original 1972 inequality has not been recognized for a long period. Hence, it would be necessary to seek such relationship. In this paper, we give several generalizations of the 1984 inequality and some known applications in order to clarify the close relationship among them. Some new types of minimax inequalities are added.