Maximal Elements and Generalized Games Involving Condensing Mappings in Locally FC-Uniform Spaces and Applications(Ⅱ)
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摘要: 在局部FC-一致空间内,引入和研究了某些新的涉及凝聚集值映象的广义矢量拟平衡问题组.应用作者在文(Ⅰ)中对局部FC-一致空间内的凝聚集值映象得到的极大元存在性定理,在局部FC-一致空间内,对这些广义矢量拟平衡问题组的解,证明了某些新的存在性定理.这些结果改进和推广了文献中某些已知结果到局部FC-一致空间.
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关键词:
- 广义矢量拟平衡问题组 /
- 极大元 /
- Ci(x)-FC-对角拟凸 /
- Ci(x)-FC-拟凸 /
- Ci(x)-FC-拟似凸 /
- 局部FC-一致空间
Abstract: Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings were introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems were proved in locally FC-uniform spaces. These results improve and generalize some recent known results in literature to locally FC-uniform spaces. -
[1] Lin L J,Liu Y H.Existence theorems for systems of generalized vector quasi-equilibrium problems and optimization problems[J].J Optim Theory Appl,2006,130(3):461-475. [2] Lin L J,Chen L F, Ansari Q H. Generalized abstract economy and systems of generalized vector quasi-equilibrium problems[J/OL]. J Comput Appl Math,2006.DOI: 10.1016/j.cam.2006.10.002. [3] Lin L J. Systems of generalized quasivariational inclusions problems with applications to variational analysis and optimizations[J].J Globbal Optim,2007,38(1):21-39. doi: 10.1007/s10898-006-9081-5 [4] Peng J W, Lee H W J, Yang X M. On system of generalized vector quasi-equilibrium problems with set-valued maps[J].J Global Optim,2006,36(1):139-158. doi: 10.1007/s10898-006-9004-5 [5] DING Xie-ping. System of generalized vector quasi-equilibrium problems on product FC-spaces[J].Acta Math Sci B,2007,27(3):522-534. [6] DING Xie-ping. The generalized game and the system of generalized vector quasi-equilibrium problems in locally FC-uniform spaces[J/OL]. Nonlinear Anal,2007.DOI: 10.1016/j.na.1006.12.003. [7] DING Xie-ping, Yao J C. Maximal element theorems with applications to generalized game and system of generalized vector quasi-equilibrium problems in G-convex spaces[J].J Optim Theory Appl,2005,126(3):571-588. doi: 10.1007/s10957-005-5498-0 [8] Lin L J. System of generalized vector quasi-equilibrium problems with applications to fixed point theorems for a family of nonexpansive multivalued mappings[J].J Global Optim,2006,34(1):15-32. doi: 10.1007/s10898-005-4702-y [9] DING Xie-ping,Yao J C, Lin L J. Solutions of system of generalized vector quasi-equilibrium problems in locally G-convex uniform spaces[J].J Math Anal Appl,2004,292(2):398-410. [10] DING Xie-ping. System of generalized vector quasi-equilibrium problems in locally FC-spaces[J].Acta Math Sinica,2006,22(5):1529-1538. doi: 10.1007/s10114-005-0671-9 [11] 丁协平.局部FC-一致空间内凝聚映象的极大元和广义对策及应用(Ⅰ)[J].应用数学和力学,2007,28(12):1392-1399. [12] Ben-El-Mechaiekh H, Chebbi S, Flornzano M,et al.Abstract convexity and fixed points[J].J Math Anal Appl,1998,222(1):138-150. doi: 10.1006/jmaa.1998.5918 [13] Horvath C. Contractibility and general convexity[J].J Math Anal Appl,1991,156(2):341-357. doi: 10.1016/0022-247X(91)90402-L [14] Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(2):551-571. doi: 10.1006/jmaa.1997.5388 [15] 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 [16] Dugundji J.Topology[M].Boston:Allyn and Bacon,Inc,1966. [17] Aliprantis C D, Border K C.Infinite Dimensional Analysis[M].New York:Springer-Verlag,1994. [18] DING Xie-ping. Generalized KKM type theorems in FC-spaces with applications(Ⅱ)[J].J Global Optim,2007,38(3):367-385. doi: 10.1007/s10898-006-9070-8 [19] DING Xie-ping, Park J Y. Generalized vector equilibrium problems in generalized convex spaces[J].J Optim Theory Appl,2004,120(2):937-990.
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