Systems of Generalized Quasi-Variational Inclusion (Disclusion) Problems in FC-Spaces
-
摘要: 应用丁协平在FC-空间内对集值映象证明的极大元存在性定理,在没有凸性结构的FC-空间内对广义拟变分包含(不包含)问题组的解证明了某些新的存在性定理.这些结果在较弱的条件下改进和推广了最近文献中的某些结果从拓朴矢量空间的闭凸子集到FC-空间.
-
关键词:
- 极大元 /
- 广义拟变分包含(不包含)问题组 /
- 部分对角拟凸 /
- 部分对角拟凹 /
- FC-空间
Abstract: By applying an existence theorem of maximal elements of setvalued mappings in FC-spaces due to the author, some new existence theorems of solutions for systems of genera-lized quasivariational in clusion(disclusion) problems were proved in FC-spaces without convexity structure. These results miprove and generalize some results in recent literature from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions. -
[1] Robinson S M.Generalized equation and their solutions[J].Math Program Study, 1979, 10(1):128-141. doi: 10.1007/BFb0120850 [2] Hassouni A, Moudafi A. A perturbed algorithm for variational inclusions[J].J Math Anal Appl, 1994, 185(3):706-721. doi: 10.1006/jmaa.1994.1277 [3] Adly S.Perturbed algorithms and sensitivity analysis for a general class of variational inclusions[J].J Math Anal Appl, 1996, 201(3):609-630. doi: 10.1006/jmaa.1996.0277 [4] DING Xie-ping.Perturbed proximal point algorithm for generalized quasivariational inclusions[J].J Math Anal Appl, 1997, 210(1):88-101. doi: 10.1006/jmaa.1997.5370 [5] 丁协平.一类广义非线性隐拟变分包含[J].应用数学和力学, 1999, 20(10):1015-1024. [6] DING Xie-ping.Perturbed Ishikawa type iterative algorithm for generalized quasivariational inclusions[J].Appl Math Comput, 2003, 141(1):359-373. doi: 10.1016/S0096-3003(02)00261-8 [7] FANG Ya-ping, HUANG Nan-jing. H-monotone operator and resolvent operator technique for variational inclusions[J].Appl Math Computat,2003, 145(3):795-803. doi: 10.1016/S0096-3003(03)00275-3 [8] DING Xie-ping.Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions[J].Appl Math Lett, 2004, 17(2): 225-235. doi: 10.1016/S0893-9659(04)90036-5 [9] DING Xie-ping, YAO Jen-chih C.Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces[J].Comput Math Appl, 2005, 49(5/6):857-869. doi: 10.1016/j.camwa.2004.05.013 [10] DING Xie-ping.Predictor-Corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusion[J].J Comput Appl Math, 2005, 182(1): 1-12. doi: 10.1016/j.cam.2004.11.036 [11] DING Xie-ping.Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings[J].J Comput Appl Math, 2005, 182(2): 252-269. doi: 10.1016/j.cam.2004.11.048 [12] Mordukhovich B S.Variational Analysis and Generalized Differentiation[M].Vol I, II, New York:Springer-Verlag, 2006. [13] LIN Lai-jiu.Systems of generalized quasivariational inclusions problems with applications to variational analysis and optimization problems[J].J Glob Optim, 2007, 38(1):21-39. doi: 10.1007/s10898-006-9081-5 [14] LIN Lai-jiu, TU Chin-I.The studies of systems of variational inclusions problems and applications[J].Nonlinear Anal, 2008, 69(7): 1981-1987. doi: 10.1016/j.na.2007.07.041. [15] 丁协平.乘积FC-空间内涉及一较好容许集值映象的优化映象的极大元及其应用[J].应用数学和力学, 2006, 27(12):1405-1416. [16] DING Xie-ping.Maximal elements of GKKM-majorized mappings in product FC-spaces and applications[J].Nonlinear Anal, 2007,67(3):963-973. doi: 10.1016/j.na.2006.06.037 [17] 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 [18] 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 [19] Horvath C D.Contractibility and generalized convexity[J].J Math Anal Appl,1991, 156(2):341-357. doi: 10.1016/0022-247X(91)90402-L [20] 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 [21] Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York: Wiley, 1984. [22] Aliprantis C D, Border K C.Infinite Dimensional Analysis[M].New York: Springer-Verlag,1994.
点击查看大图
计量
- 文章访问数: 1171
- HTML全文浏览量: 76
- PDF下载量: 753
- 被引次数: 0