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

丁协平¹, 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

收稿日期:2001-06-12 修回日期:2002-07-20 出版日期:2002-11-18 发布日期:2002-11-18
基金资助:
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)

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)

摘要/Abstract

摘要： 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.

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

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

中图分类号:

O177.92

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

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

参考文献

[1] Tarafdar E. A fixed point theorem and equilibrium point of an abstract economy[J]. J Math Econom, 1991,20(2):211-218.
[2] LAN Kun-Quan, Webb J. New fixed point theorems for a family of mappings and applications to problems on sets with convex secfions[J]. Proc Amer Math Soc, 1998,126(4): 1127-1132.
[3] Ansari Q H, Yao J C. A fixed point theorem and its applications to a system of variational inequalities[J]. Bull Austral Math Soc, 1999 ,59(2):433-442.
[4] Singh S P, Taraf dar E, Watson B. A generalized fixed point theorem and equilibrium point of anabstract economy[J]. J Computat Appl Math, 2000,113 (1/2):65-71.
[5] Taraf dar E. Fixed point theorems in H-spaces and equilibrium point of abstract economies[J]. J Austral Math Soc Ser A, 1992,53(2):252-260.
[6] CHANG Shi-sheng, Lee B S, Cho Y J, et al. On the generalized quasi-variational inequality problems[J]. J Math Anal Appl, 1996,203(3):686-711.
[7] LIN Lai-jiu, Park S. On some generalized quasi-equilibrium problems[J]. J Math Anal Appl, 1998,224(1): 167-181.
[8] Patk S. Continuous selection theorems in generalized convex spaces[J]. Numer Funct Anal Optimiz, 1999,20 (5/6): 567-583.
[9] DING Xie-ping. New H-KKM theorems and their applications to geometric property, coincidence theorems, minimax inequality and maximal elements[J]. Indian J Pure Appl Math, 1995,26 (1): 1-19.
[10] DING Xie-ping. Generalized variational inequalities and equilibrium problems in generalized convex spaces[J]. Computers Math Applic, 1999,38(7/8): 180-197.
[11] Wilansky A. Topology for Analysis[M]. Waltham Massachusetts: Ginn, 1972.
[12] Dugundji J. Topology[M]. Boston: Allyn and Bacon Inc, 1966.
[13] Husain T. Topology and Maps[M]. New York: Plenum Press,1977.
[14] Kelley J L. General Topology[M]. Princeton:D Van Nostrand Co, 1955.
[15] Park S, Kim H. Coincidence theorems for admissible multifunctions on generalized convex spaces[J]. J Math Anal Appl,1997,197(1):173-187.
[16] Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J]. J Math Anal Appl, 1997,209(2):551-571.
[17] Ben-E1-Mechaiekh H, Chebbi S, Flornzano M, et al. Abstract convexity and fixed points[J]. J Math Anal Appl, 1998,222(1): 138-150.
[18] Tychonoff A. Ein fixpunktsatz[J]. Math Ann, 1935,111:767-776.
[19] DING Xie-ping. Coincidence theorems in topological spaces and their applications[J]. Appl Math Lett, 1999,12(7):99-105.
[20] Taraf dar E. A fixed point theorem equivalent to the Fan-Knastre-Kuratowski-Mazurkiewicz theorem[J]. J Math Anal Appl, 1987,128(3):475-479.
[21] Shih M H, Tan K K. Non-compact sets with convex sections[J]. Pacific J Math, 1985,119(2): 473-479.
[22] Fan Ky. Some properties of convex sets related fixed point theorems[J]. Math Ann, 1984,266(3): 519-527.
[23] Ma TW. On sets with convex sections[J]. JMathAnalAppl,1964,27(2):413-416.
[24] Fan Ky. Applications of a theorem concerning sets with convex sections[J]. Math Ann, 1966,163 (2): 189-203.
[25] DI2G Xie-ping, Kim W K, Tan K K. Equilibria of noncompact generalized games with * majorized preference correspondences[J]. J Math Anal Appl, 1992,164 (3): 508-517.
[26] DING Xie-ping, Kim W K, Tan K K. A selection theorem and its application[J]. Bull Austral Math Soc, 1992,46(2):205-212.
[27] DING Xie-ping, Tan K K. On equilibria of norcompact generalized games[J]. J Math Anal Appl, 1993,177(1):226-238.

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

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

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