关于一般化凸乘积空间上的极大元和平衡点On maximal elements and equilibrium points on generalized convex product spaces
朴勇杰;姜今锡;钟立楠;
摘要(Abstract):
利用一般化凸乘积空间上的Fan-Browder型不动点定理给出了新的极大元存在定理,然后定义了两个概念:"类Uθ"和"类V",并讨论了在抽象经济中平衡点的存在性问题.文中所得结论改进和推广了文献中的相应结果.
关键词(KeyWords): 一般化凸空间;Γ-凸;极大元;平衡点;类Uθ;类V
基金项目(Foundation): 国家自然科学基金(10361005);; 延边大学科研项目(2004[8])
作者(Authors): 朴勇杰;姜今锡;钟立楠;
参考文献(References):
- [1]Arrow K J,Debreu D.Existence of an equilibrium for a competitive economy[J].Econometrica,1954,22:265-290.
- [2]Gale D,MasColell A.On the Role of Complete,Transitive Preference in Equilibrium Theory[M]//Schwd¨iauer G.Equilibrium and Disequilibrium in Economic Theory.Dordrecht:Reidel,1978.
- [3]Metha G,Tan K K,Yuan X Z.Fixed points,maximal elements and equilibria of generalized games[J].Nonlinear Anal.,1997,28:689-699.
- [4]Berge C.Sur une convexitéréguliere et ses applications à la théorie des jeux[J].Bull.Soc.Math.France,1954,82:301-319.
- [5]Ding X P.Equilibria of noncompact generalized games with U-majorized preference correspondences[J].Appl.Math.Lett.,1998,11:115-119.
- [6]Ding X P,Tan K K.On equilibria of non-compact generalized games[J].J.Math.Anal.Appl.,1993,177:226-238.
- [7]Ding X P,Yuan G X Z.The study of existence of equilibria for generalized games without lower semicontinuity in locally topological vector spaces[J].J.Math.Anal.Appl.,1998,227:420-438.
- [8]Lin L J,Park S H.On some generalized quasi-equilibrium problems[J].J.Math.Anal.Appl.,1998,224:167-181.
- [9]Tan K K,Wu X.A note on abstract economies with upper simicontinuous correspondence[J].Appl.Math.Lett.,1998,11:21-22.
- [10]Yuan X Z,Tarafdar E.Maximal elements and equilibria of generalized games for condensing corresponden-ces[J].J.Math.Anal.Appl.,1996,203:13-30.
- [11]Park S H.New Susclasses of Generalized Concev Spaces[M]//NY.Fixed Point Theory and Applications(Chinju,1998),91-98.Huntington:Nova Sci.Publ.,2000.
- [12]Park S H.Elements of the KKM theory for generalized convex spaces[J].Korean J.Comp.Appl.Math.,2000,7:1-28.
- [13]Lassonde M.On the use of KKM multimaps in fixed point theory and related topics[J].J.Math.Anal.Appl.,1983,97:151-201.
- [14]Horvath C D.Contractibility and generalized convexity[J].J.Math.Anal.Appl.,1991,156:341-357.
- [15]朴勇杰.Fan-Browder type fixed point and equilibrium point on generalized convex product spaces[J].纯粹数学与应用数学,2004,20(3):197-203.
- [16]朴勇杰.一般化凸空间上的一些基本性质[J].延边大学学报:自然科学版,2002,28(3):157-159.