DING Xie-ping. Maximal Elements for GB-Majorized Mappings in Product G-Convex Spaces and Applications(Ⅰ)[J]. Applied Mathematics and Mechanics, 2003, 24(6): 583-594.
Citation: DING Xie-ping. Maximal Elements for GB-Majorized Mappings in Product G-Convex Spaces and Applications(Ⅰ)[J]. Applied Mathematics and Mechanics, 2003, 24(6): 583-594.

Maximal Elements for GB-Majorized Mappings in Product G-Convex Spaces and Applications(Ⅰ)

  • Received Date: 2002-01-19
  • Rev Recd Date: 2003-02-19
  • Publish Date: 2003-06-15
  • 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.
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  • [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.
    Debreu G.A Social equilibrium existence theorem[J].Proc Nat Acad Sci USA,1952,38(1):121-126.
    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.
    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.
    Tulcea C I.On the equilibriums of generalized games[R].The Center for Math,Studies in Economics and Management Science,Paper No.696,1986.
    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.
    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.
    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.
    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.
    Ding X P,Tan K K.On equilibria of noncompact generalized games[J].J Math Anal Appl,1993,177(1):226-238.
    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.
    Ding X P.Coincidence theorems and equilibria of generalized games[J].Indian J Pure Appl Math,1996,27(11):1057-1071.
    Ding X P.Fixed points,minimax inequalities and equilibria of noncompact generalized games[J].Taiwanese J Math,1998,2(1):25-55.
    Ding X P.Equilibria of noncompact generalized games with U-majorized preference correspondences[J].Appl Math Lett,1998,11(5):115-119.
    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.
    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.
    Tan K K,Yuan X Z.Existence of equilibrium for abstract economies[J].J Math Econom,1994,23(2):243-251.
    Tan K K,Yuan X Z.Approximation method and equilibria of abstract economies[J].Proc Amer Math Soc,122(3):503-510.
    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.
    Tarafdar E.A fixed point theorem and equilibrium point of an abstract economy[J].J Math Econom,1991,20(2):211-218.
    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.
    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.
    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.
    Yuan G X-Z.KKM Theory and Application in Nonlinear Analysis[M].New York:Marcel Dekker,Inc 1999.
    Yuan G X-Z.The existence of equilibria for noncompact generalized games[J].Appl Math Lett,2000,13(1):57-63.
    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.
    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.
    Park S,Kim H.Coincidence theorems for admissible multifunctions on generalized convex spaces[J].J Math Anal Appl,1996,197(1):173-187.
    Park S,Kim H.Foundations of the KKM theory on generanized convex spaces[J].J Math Anal Appl,1997,209(3):551-571.
    Park S.Continuous selection theorems for admissible multifunctions on generalized convex spaces[J].Numer Funct Anal Optimiz,1999,25(3):567-583.
    Park S.Fixed points of admissible maps on generalized convex spaces[J].J Korean Math Soc,2000,37(4):885-899.
    Park S.Coincidence theorems for the better admissible multimaps and their applications[J].Nonlinear Anal,1997,30(12):4183-4191.
    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.
    Chang T H,Yen C L.KKM property and fixed point theorems[J].J Math Anal Appl,1996,203(1):224-235.
    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.
    Aubin J P,Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley & Sons,1984.
    Dugundji J.Topology[M].Boston:Allyn and Bacon,1966.
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