The Journal of the Indian Mathematical Society

E. Tarafdar ¹

Affiliations
1 Regional Engineering College, Durgapur, IN

Abstract

The properties of extreme points have been exhaustively dealt with in [1], [2] and [3]. In the present paper a necessary and sufficient condition for a mapping to be quasi-open in terms of extreme points is given.

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A. K. Chaudhuri ¹, E. Tarafdar ¹

Affiliations
1 Regional Engineering College, Durgapur, IN

Abstract

In this paper certain general properties of mappings from one neighborhood space to another have been discussed.

The concepts of locally strongly interior points, locally weakly interior points and extreme points of mapping have been introduced and some of their properties have been studied.

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Mohammad S. R. Chowdhury ¹, E. Tarafdar ¹, George X. Z. Yuan ¹

Affiliations
1 Department of Mathematics, The University of Queensland, Brisbane, Queensland-4072, AU

Abstract

A fixed point theorem is proved in G-convex spaces (introduced by Park and Kim [17]). As applications of the fixed point theorem some existence theorems of maximal elements for G^L_C correspondences and G^L_C majorized correspondences are obtained. Applying the existence theorems of maximal elements, some equilibrium existence theorems for one-person games, qualitative games and non-compact generalized games are given. These results are generalization, into G-convex spaces, of the corresponding results due to Border, Borglin-Keiding, Chang, Ding-Tan, Ding-Kim-Tan, Shafer-Sonnenschein, Tan-Yuan. Toussaint, Tulcea and Yannaelis-Prabhakar.

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