A minimax inequality with applications to existence of equilibrium point and fixed point theorems
Colloquium Mathematicum, Tome 63 (1992) no. 2, pp. 233-247
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.
@article{10_4064_cm_63_2_233_247,
author = {Xie Ding and Kok-Keong Tan},
title = {A minimax inequality with applications to existence of equilibrium point and fixed point theorems},
journal = {Colloquium Mathematicum},
pages = {233--247},
year = {1992},
volume = {63},
number = {2},
doi = {10.4064/cm-63-2-233-247},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-63-2-233-247/}
}
TY - JOUR AU - Xie Ding AU - Kok-Keong Tan TI - A minimax inequality with applications to existence of equilibrium point and fixed point theorems JO - Colloquium Mathematicum PY - 1992 SP - 233 EP - 247 VL - 63 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-63-2-233-247/ DO - 10.4064/cm-63-2-233-247 LA - en ID - 10_4064_cm_63_2_233_247 ER -
%0 Journal Article %A Xie Ding %A Kok-Keong Tan %T A minimax inequality with applications to existence of equilibrium point and fixed point theorems %J Colloquium Mathematicum %D 1992 %P 233-247 %V 63 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/cm-63-2-233-247/ %R 10.4064/cm-63-2-233-247 %G en %F 10_4064_cm_63_2_233_247
Xie Ding; Kok-Keong Tan. A minimax inequality with applications to existence of equilibrium point and fixed point theorems. Colloquium Mathematicum, Tome 63 (1992) no. 2, pp. 233-247. doi: 10.4064/cm-63-2-233-247
Cité par Sources :