NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (11): 1237-1249.

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NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

DING Xie-ping¹, Park Jong-yeoul²

1. Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China;
2. Department of Mathematics, Pusan National University Kumjung, Pusan 609-735, Korea

Received:2001-06-12 Revised:2002-07-20 Online:2002-11-18 Published:2002-11-18
Supported by:
the National Natural Science Foundation of China(19871059);the KOSEFof Korea and the Natural Science Foundation of the Education Department of Sichuan Province of China([2000]25);the Korea Research Foundation(1998-15-D00021)

Abstract

Abstract: By applying the technique of continuous partition of unity and Tychonoff’s fixed point theorem, some new collectively fixed point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G-convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces. Our theorems improve, unify and generalized many important known results in recent literature.

Key words: collectively fixed point, nonempty intersection theorem, system of inequality, abstract economy, generalized convex space

2010 MSC Number:

O177.92

DING Xie-ping;Park Jong-yeoul. NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES. Applied Mathematics and Mechanics (English Edition), 2002, 23(11): 1237-1249.

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NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

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