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广义投影下F隐变分不等式解的存在性 被引量：3

Existence of Solutions of F-Implicit Variational Inequality Problems with Extended Projection Operators
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摘要 首先引进了广义(F,g)-投影算子,提出了一个新的例外簇概念,并运用Fan-KKM定理以及例外簇,分别在无单调性与渐近h-g伪单调假设下,研究了自反Banach空间中一类F隐变分不等式的可解性与解集特征问题,得到了新的解的存在性定理. In this paper, the authors investigate a class of F-implicit variational inequality problems in reflexive Banach spaces. By introducing a new concept of the generalized （F, g）-projection operator and a new definition of exceptional family and using Fan-KKM theorem and exceptional family under asymptotic h-g pseudomonotonieity and without monotonicity assumptions, respectively, the authors derive some existence theorems and some properties of the solutions.
作者 陈加伟 邹云志
机构地区 西华师范大学数学与信息学院 四川大学数学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2010年第2期375-384,共10页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(60804065) 四川省教育厅重点项目(07ZA123) 西华师范大学科研启动基金资助项目(08B075)
关键词 F隐变分不等式 例外簇 J-g全连续场 F-implicit variational inequality exceptional family J-g completely continuous field
分类号 O177.91 [理学—基础数学]
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参考文献15

  • 1Yin H. Y., Xu C. X., Zhang Z. X., The F-complementarity problems and its equivalence with the least element problem, Acta Mathematica Sinica, Chinese Series, 2001, 44(4): 679-686.
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同被引文献21

  • 1方亚平,黄南京.不具单调性的均衡系统问题的解的存在性[J].数学物理学报（A辑）,2005,25(6):763-769. 被引量：2
  • 2Yin H Y,Xu C X,Zhang Z X.The complementarity problems and its equivalence with the least element problem[J].Acta Math.Sinica,2001 (44):679-686.
  • 3Huang N J,Fang Y P.Fixed point theorems and a new system of multivalued generalized order complementarity problems[J].Positivity,2003(7):257-265.
  • 4Kassay G,Kolumbdn J.System of multivalued variational inequalities[J].Publ Math Debrecen,2000(56):185-195.
  • 5Verma R U.A system of generalized auxiliariy problems principle and a system of variational inequalities[J].Math.Ineq&Appl,2001(4):443-453.
  • 6Verma R U.Projection methods,algorithems and a new system of nonlinear variational inequalities[J].Comput,Appl.Math,2001(41):1025-1031.
  • 7Fang Y P, Huang N J. Variational-like inequalities with generalized monotone mapping in Banach spaces spaces[J]. Optim. Theory Appl., 2003 (118):327-338.
  • 8Fan K. A generalization of Tychonoff's fixed point theorem[J]. Math, Ann., 1961 (142): 305-310.
  • 9Bai M R S, Zhou Z, Ni G Y. Variational-like inequalities with η-α pseudomonotone mappings in Banach spaces[J]. Appl. Math. Lett., 2006 (19):547-554.
  • 10Vera R U. On monotone nonlinear varational inequalities problems[J]. Comment. Math. Univ.Carolin. 1998, 39: 91-98.

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数学学报（中文版）
2010年 第2期

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