Maximal Elements for GB-Majorized Mappings in Product G-Convex Spaces and Applications(Ⅱ)
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摘要: 通过应用G-凸空间的乘积空间内一族GB-优化映象的极大元的存在定理,在G-凸空间的非紧设置下证明了某些重合点定理,Fan-Browder型不动点定理和极小极大不等式组的解的存在性定理。这些定理改进和推广了文献中许多重要的已知结果。
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关键词:
- 极大元 /
- GB-优化映象族 /
- 重合定理 /
- 极小极大不等式 /
- G-凸空间的乘积空间
Abstract: By applying existence theorems of maximal elements for a family of GB-majorized map-pings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature. -
[1] 丁协平.乘积G-凸空间内的GB-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. [2] 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. [3] Deguire P,Lassonde M.Familles sélectantes[J].Topol Methods Nonlinear Anal,1995,5:261-269. [4] Deguire P.Brewder-Fan fixed point theorem and relatd results[J].Discuss Math Differential Incl,1995,15:149-162. [5] Ben-El-Mechaiekh H,Deguire P,Granas A.Points fixeset coincidences pour lesapplications multivoques(applications de Ky Fan)[J].C R Acad Sci Paris,1982,295:337-340. [6] Ben-El-Mechaiekh H,Deguire P,Granas A.Points fixeset coincidences pour lesapplications multivoques(applications de Øand Ø*)[J].C R Acad Sci Paris,1982,295:381-384. [7] Lassonde M.On the use of KKM multifunctions in fixedpoint theory and related topics[J].J Math Anal Appl,1983,97:151-201. [8] Lassdone M.Fixed point for Kakutani factorizable multifunctions[J].J Math Anal Appl,1990,152:46-60. [9] Tarafdar E.A fixed points theorem and equilibrium point of abstract economy[J].J Math Econom,1991,20(2):211-218. [10] Tarafdar E.Fixed point theorems in H-spaces and equilibrium points of abstract economics[J].J Austral Math Soc,Ser A,1992,53:252-260. [11] DING Xie-ping.Tarafdar E.Some coincidence theorems and applications[J].Bull Austral Math Soc,1994,50:73-80. [12] DING Xie-ping,Tarafdar E.Fixed point theorem and existence of equilibrium points of noncompact abstract economies[J].Nonlinear World,1994,1:319-340. [13] DING Xie-ping.New H-KKM theorems and their applications to gemectric property,coincidence theorems,minimax inequality and maximal elements[J].Indian J Pure Appl Math,1995,26(1):1-19. [14] DING Xie-ping.Fixed points,minimax inequalities and equilibria of noncompact abstract economies[J].Taiwanese J Math,1998,2(1):25-55. [15] Fan Ky.A minimax inequality and applications[A].In:Shisha O Ed.Inequality Ⅲ[C].New York:Academic Press,1972. [16] Fan Ky.Some properties of convex sets related to fixed point theorems[J].Math Ann,1984,266:519-537.
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