MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (6): 659-672.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

丁协平

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China

收稿日期:2002-01-19 修回日期:2003-02-19 出版日期:2003-06-18 发布日期:2003-06-18
基金资助:
the National Natural Science Foundation of China(19871059);the Natural Science Foundation of Education Department of Sichuan Province of China([2000]25)

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

DING Xie-ping

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China

Received:2002-01-19 Revised:2003-02-19 Online:2003-06-18 Published:2003-06-18
Supported by:
the National Natural Science Foundation of China(19871059);the Natural Science Foundation of Education Department of Sichuan Province of China([2000]25)

摘要/Abstract

摘要： A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.

中图分类号:

O177.92

丁协平. MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(6): 659-672.

DING Xie-ping. MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(6): 659-672.

参考文献

[1] Borglin A,Keiding H.Existence of equilibrium actions and of equilibrium:A note on the "new " existence theorems[J].J Math Econom,1976,3(2):313-316.
[2] Debreu G.A Social equilibrium existence theorem[J].Proc Nat Acad Sci USA,1952,38(1):121-126.
[3] Yannelis N C,Prabhakar N D.Existence of maximal elements and equilibria in linear topological spaces[J].J Math Econom,1983,12(2):233-245.
[4] Toussaint S.On the existence of equilibra in economies with infinite commodities and without ordered preferences[J].J Econom Theory,1984,33(1):98-115.
[5] Tulcea C I.On the equilibriums of generalized games[R].The Center for Math,Studies in Economics and Management Science,Paper No.696,1986.
[6] Tulcea C I.On the approximation of upper semi-continuous correspondences and the equilibriums of generalized games[J].J Math Anal Appl,1988,136(2):267-289.
[7] Ding X P,Kim W K,Tan K K.Equilibria of noncompact generalized games with L^*-majorized preference correspondences[J].J Math Anal Appl,1992,162(3):508-517.
[8] Ding X P,Kim W K,Tan K K.Equilibria of generalized games with L-majorized correspondences[J].Internat J Math Math Sci,1994,17(4):783-790.
[9] Ding X P,Tan K K.A minimax inequality with applications to existence of equilibrium point and fixed point theorems[J].Colloq Math,1992,63(1):233-247.
[10] Ding X P,Tan K K.On equilibria of noncompact generalized games[J].J Math Anal Appl,1993,177(1):226-238.
[11] Ding X P,Tarafdar E.Fixed point theorems and existence of equilibrium points of noncompact abstract economies[J].Nonlinear World,1994,1(1):319-340.
[12] Ding X P.Coincidence theorems and equilibria of generalized games[J].Indian J Pure Appl Math,1996,27(11):1057-1071.
[13] Ding X P.Fixed points,minimax inequalities and equilibria of noncompact generalized games[J].Taiwanese J Math,1998,2(1):25-55.
[14] Ding X P.Equilibria of noncompact generalized games with U-majorized preference correspondences[J].Appl Math Lett,1998,11(5):115-119.
[15] Ding X P.Maximal element principles on generalized convex spaces and their application[A].In:R P Argawal Ed.Ser Math Anal Appl[C].London:Taylor and Francis,2002,149-174.
[16] Ding X P,Yuan G X-Z.The study of existence of equilibria for generalized games without lower semicontinuity in locally convex topological vector spaces[J].J Math Anal Appl,1998,227(2):420-438.
[17] Tan K K,Yuan X Z.Existence of equilibrium for abstract economies[J].J Math Econom,1994,23(2):243-251.
[18] Tan K K,Yuan X Z.Approximation method and equilibria of abstract economies[J].Proc Amer Math Soc,122(3):503-510.
[19] Tan K K,Zhang X L.Fixed point theorems on G-convex spaces and applications[J].Proc Nonlinear Funct Anal Appl,1996,1(1):1-19.
[20] Tarafdar E.A fixed point theorem and equilibrium point of an abstract economy[J].J Math Econom,1991,20(2):211-218.
[21] Tarafdar E.Fixed point theorems in H-spaces and equilibrium points of abstract economies[J].J Austral Math Soc,Ser A,1992,53(1):252-260.
[22] Yuan G X-Z.The study of minimax inequalities and applications to economies and variational inequalities[J].Mem Amer Math Soc,1998,132(625):1-132.
[23] Deguire P,Tan K K,Yuan X Z.The study of maximal elements, fixed points for LS-majorized mappings and their applications to minimax and variational inequalities in product topological spaces[J].Nonlinear Anal,1999,37(8):933-951.
[24] Yuan G X-Z.KKM Theory and Application in Nonlinear Analysis[M].New York:Marcel Dekker,Inc 1999.
[25] Yuan G X-Z.The existence of equilibria for noncompact generalized games[J].Appl Math Lett,2000,13(1):57-63.
[26] Shen Z F.Maximal element theorems of H- majorized correspondence and existence of equilibrium for abstract economies[J].J Math Anal Appl,2001,256(1):67-79.
[27] Singh S P,Tarafdar E,Watson B.A generalized fixed point theorem and equilibrium point of an abstract economy[J].J Computat Appl Math,2000,113(1):65-71.
[28] Park S,Kim H.Coincidence theorems for admissible multifunctions on generalized convex spaces[J].J Math Anal Appl,1996,197(1):173-187.
[29] Park S,Kim H.Foundations of the KKM theory on generanized convex spaces[J].J Math Anal Appl,1997,209(3):551-571.
[30] Park S.Continuous selection theorems for admissible multifunctions on generalized convex spaces[J].Numer Funct Anal Optimiz,1999,25(3):567-583.
[31] Park S.Fixed points of admissible maps on generalized convex spaces[J].J Korean Math Soc,2000,37(4):885-899.
[32] Park S.Coincidence theorems for the better admissible multimaps and their applications[J].Nonlinear Anal,1997,30(12):4183-4191.
[33] Park S.A unified fixed point theory of multimaps on topological vector spaces[J].J Korean Math Soc,1998,35(4):803-829.Corrections,ibid,1999,36(4):829-832.
[34] Chang T H,Yen C L.KKM property and fixed point theorems[J].J Math Anal Appl,1996,203(1):224-235.
[35] Ben-El-Mechaiekh H,Chebbi S,Florenzano M,et al.Abstract convexity and fixed points[J].J Math Anal Appl,1998,222(1):138-151.
[36] Aubin J P,Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley & Sons,1984.
[37] Dugundji J.Topology[M].Boston:Allyn and Bacon,1966.

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	邓磊;臧小燕. FC_空间中的参数型KKM定理及其应用[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 73-79 .
[2]	臧小燕;邓磊. Iterative algorithm of solutions for multivalued general mixed implicit equilibrium-like problems[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(4): 477-484 .
[3]	方敏;丁协平. GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN FC-SPACES[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(11): 1451-1459 .
[4]	丁协平;林炎诚;姚任之. PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(9): 1157-1164 .
[5]	彭建文;杨新民;朱道立. SYSTEM OF VECTOR QUASI-EQUILIBRIUM PROBLEMS AND ITS APPLICATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(8): 1107-1114 .
[6]	宋长明. NONEXISTENCE OF GLOBAL SOLUTIONS OF NONLINEAR HYPERBOLIC EQUATION WITH MATERIAL DAMPING[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(7): 975-981 .
[7]	丁协平. SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅰ)[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(12): 1547-1555 .
[8]	丁协平. SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅱ)[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(12): 1556-1563 .
[9]	丁协平. NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(6): 618-626.
[10]	丁协平. MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅱ)[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 1017-1024.
[11]	魏鸣;刘国庆;王成刚;葛文忠;许秦. OPTIMAL SELECTION FOR THE WEIGHTED COEFFICIENTS OF THE CONSTRAINED VARIATIONAL PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(8): 936-944.
[12]	丁协平. CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY CONVEX H-SPACES[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(5): 499-508.
[13]	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.
[14]	丁协平;夏福全. GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(10): 1140-1148.
[15]	扶名福;吴洪飞. THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF GENERALIZED VARIATIONAL INEQUALITIES ARISING FROM ELASTICITY WITH FRICTION[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(8): 929-936.