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广义f-投影算子的稳定性及其应用 被引量：1

On the Stability of Generalized f-Projection Operators with an Application
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摘要 在Banach空间中,本文研究广义f-投影算子关于集合扰动的稳定性.作为应用,本文在Banach空间中运用广义f-投影算子解决了一类广义变分不等式问题. In this paper, the stability of generalized f-projection operators with a perturbation of the set is studied in Banach spaces. As an application, a perturbed iterative algorithm involving the generalized f-projection operator for solving a class of generalized variational inequality problem in Banach spaces is constructed.
作者 李曦 黄南京 邹云志
机构地区 四川大学数学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2011年第5期811-822,共12页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金重点项目(70831005) 国家自然科学基金资助项目(10671135)
关键词 广义f-投影算子 凸性模 广义变分不等式 generalized f-projection operator convexity modulus generMized variational inequality
分类号 O224 [理学—运筹学与控制论]
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参考文献18

  • 1Alber Ya., Generalized projection operators in Banach spaces: Properties and applications, in: Proceedings of the Israel Seminar, Ariel, Israel, Funct. Differential Equation, 1994, 1: 1-21.
  • 2Alber Ya., Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications, in: A. G. Kartsatos (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, New York: Marcel Dekker, 1996:15 50.
  • 3Li J., The generalized projection operator on reflexive Banach spaces and its application, J. Math. Anal. Appl., 2005, 306: 377-388.
  • 4Chen J. W., Zou Y. Z., Existence of solutions of F-implicit variational inequality problems with extended projection operators, Acta Mathematica Sinica, Chinese Series, 2010, 53(2): 375-384.
  • 5Alber, Ya., On the Stability of iterative approximations to fixed points of nonexpansive mappings, J. Math. Anal. Appl., 2007, 328:958 971.
  • 6Alber Ya., Yao J. C., Another version of the proximal piont algorithm in a Banach space, Nonlinear Anal. TMA, 2009, 70:3159 3171.
  • 7Wu K. Q., Huang N. J., The generalised f-projection operator with an apllication, Bull. Austral. Math. Soc., 2006, 73:307 317.
  • 8Wu K. Q., Huang N. J., Properties of the generalized f-projection operator and its applications in Banach spaces, Uomput. Math. Appl., 2007, 54: 399-406.
  • 9Wu K. Q., Huang N. J., The generalized f-projection operator and set-valued variational inequalities in Banach spaces, Nonlinear Anal. TMA, 2009, 71: 2481-2490.
  • 10Fan J. H., Liu X., Li J., Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Anal. TMA, 2009, 70:3997 4007.

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数学学报（中文版）
2011年 第5期

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