Maximal Elements of a Family of Majorized MappingsInvolving a Better Admissible Mapping in Product FC-Spaces and Applications

DING Xie-ping

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(12): 1405-1416

DING Xie-ping. Maximal Elements of a Family of Majorized MappingsInvolving a Better Admissible Mapping in Product FC-Spaces and Applications[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1405-1416.

Citation:

PDF( 507 KB)

Maximal Elements of a Family of Majorized MappingsInvolving a Better Admissible Mapping in Product FC-Spaces and Applications

DING Xie-ping

College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China

Received Date: 2005-04-16
Rev Recd Date: 2006-08-10
Publish Date: 2006-12-15

Abstract

Abstract

A new family of majorized mappings from a topological space into a finite continuous topological space (in short, FC-space) involving a better admissible set-valued mapping was introduced. Some existence theorems of maximal elements for the family of majorized mappings were proved under noncompact setting of product FC-spaces. Some applications to fixed point and system of minimax inequalities were given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.

FullText(HTML)

References(19)

References

[1]	DING Xie-ping.Maximal element theorems in product FC-spaces and generalized games[J].J Math Anal Appl,2005,305(1):29—42. doi: 10.1016/j.jmaa.2004.10.060
[2]	Lassonde M. On the use of KKM multifunctions in fixed point theory and related topics[J].J Math Anal Appl,1983,97(1):151—201. doi: 10.1016/0022-247X(83)90244-5
[3]	Horvath C D.Contractibility and general convexity[J].J Math Anal Appl,1991,156(2):341—357. doi: 10.1016/0022-247X(91)90402-L
[4]	Park S, Kim H.Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(3):551—571. doi: 10.1006/jmaa.1997.5388
[5]	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. doi: 10.1006/jmaa.1998.5918
[6]	DING Xie-ping.Maximal element principles on generalized convex spaces and their application[A].In:Argawal R P,Ed.Set Valued Mappings With Applications in Nonlinear Analysis[C].in:SIMMA,Vol 4,2002,149—174.
[7]	丁协平.乘积G-凸空间内的GB[KG*9]. -优化映象的极大元及其应用(Ⅰ)[J].应用数学和力学，2003，24(6)：583—594.
[8]	丁协平.乘积G-凸空间内的GB[KG*9]. -优化映象的极大元及其应用(Ⅱ)[J].应用数学和力学，2003，24(9)：899—905.
[9]	Deguire P,Tan K K,Yuan X Z.The study of maximal elements,fixed points for LS—majorized mappings and their applications to minimax and variational inequalities in product topological spaces[J].Nonlinear Anal,1999,37(7):933—951. doi: 10.1016/S0362-546X(98)00084-4
[10]	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. doi: 10.1006/jmaa.2000.7285
[11]	Dugundji J.Topology[M].Boston:Allyn and Bacon,1966.
[12]	Aubin J P,Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley & Sons,1984.
[13]	Yannelis N C,Prabhakar N D.Existence of maximal elements and equilibria in linear topological spaces[J].J Math Econom,1983,12(3):233—245. doi: 10.1016/0304-4068(83)90041-1
[14]	DING Xie-ping, Tan K K.On equilibria of noncompact generalized games[J].J Math Anal Appl,1993,177(1):226—238. doi: 10.1006/jmaa.1993.1254
[15]	DING Xieping,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. doi: 10.1155/S0161171294001092
[16]	Tulcea C I. On the equilibriums of generalized games[R]. The Center for Math Studies in Economics and Management Science, paper No 696,1986.
[17]	Toussaint S. On the existence of equilibria in economies with infinite commodities and without ordered preferences[J].J Econom Theory,1984,33(1):98—115. doi: 10.1016/0022-0531(84)90043-7
[18]	Borglin A,Keiding H.Existence of equilibrium actions and of equilibrium: A note on the “new” existence theorems[J].J Math Econom,1976,3(3):313—316. doi: 10.1016/0304-4068(76)90016-1
[19]	DING Xie-ping.Fixed points, minimax inequalities and equilibria of noncompact generalized games[J].Taiwanese J Math,1998,2(1):25—55.[JP3]. DING Xie-ping,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. doi: 10.1006/jmaa.1998.6105