Abstract
In this article, by virtue of the Kakutani-Fan-Glicksberg fixed point theorem, two types of Ky Fan minimax inequalities for set-valued mappings are obtained. Some examples are given to illustrate our results.Mathematics Subject Classification (2010): 49J35; 49K35; 90C47.
Highlights
1 Introduction It is well known that Ky Fan minimax inequalities play a very important role in many fields, such as variational inequalities, game theory, mathematical economics, control theory, and fixed point theory
Because of its wide applications, Ky Fan minimax inequalities have been generalized in various ways
In recent years, based on the development of vector optimization, a great deal of articles have devoted to the study of the Ky Fan minimax theorems for vector-valued functions
Summary
It is well known that Ky Fan minimax inequalities play a very important role in many fields, such as variational inequalities, game theory, mathematical economics, control theory, and fixed point theory. Li and Wang [7] established the following Ky Fan minimax inequalities for vector-valued mappings: Minw Maxwf (x, X0) ⊂ Max f (x, x) − S, x∈X0 x∈X0 Max Minwf (x, Y0) ⊂ Min Maxwf (X0, y) + S, x∈X0 y∈Y0 where the vector-valued function is f(x, y) = x + y.
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