A minimax inequality with applications to existence of equilibrium point and fixed point theorems

• Autorzy: Xie Ping Ding , Kok-Keong Tan
• Języki publikacji: EN

Abstrakty

EN

Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an equilibrium point in a one-person game. Next, by applying the minimax inequality, we present some fixed point theorems for set-valued inward and outward mappings on a non-compact convex set in a topological vector space. These results generalize the corresponding results due to Browder [5], Jiang [11] and Shih Tan [15] in several aspects.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1992
• Tom: 63
• Numer: 2
• Strony: 233-247

Daty

wydano

1992

otrzymano

1990-02-07

poprawiono

1991-03-04

Twórcy

autor

Xie Ping Ding

• Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, China,

autor

Kok-Keong Tan

• Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada, B3h 3j5

Bibliografia

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• [3]J. S. Bae, W. K. Kim and K. K. Tan, Another generalization of Fan's minimax inequality and its applications, submitted.
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