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Banach空间中一类广义变分不等式的强收敛定理

STRONG CONVERGENCE THEOREMS FOR A GENERALIZED VARIATIONAL INEQUALITIE IN BANACH SPACES
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摘要 应用广义f-投影算子引入了一类新的迭代方法,并用此方法在Banach空间的非紧子集上证明了一个关于一类广义变分不等式的强收敛定理;该定理中所涉及到的映射既不具备紧性也不具备单调性。所得结果推广了最近一些相关定理。 By using the generalized f-projection operator and the monotone hybrid pro- jection method, we introduce a new iterative sequence for finding a solution of a generalized variational inequality. Moreover, we obtain a strong convergence theorem for the generalized variational inequality in noncompact subsets of Banach spaces without assuming the compact- ness of mappings. Conditions on the theorem are weaker than those of recent some related theorems. The conclusions extend and develop previous related results.
作者 刘英
机构地区 河北大学数学与计算机学院
出处 《系统科学与数学》 CSCD 北大核心 2012年第5期591-600,共10页 Journal of Systems Science and Mathematical Sciences
基金 河北省自然科学基金资助项目(A2011201053 A2010000191) 河北省教育厅自然科学基金资助项目(2010110) 国家自然科学基金资助项目(11101115)
关键词 广义变分不等式 柯西列 广义f-投影 连续性 Generalized variational inequalities, Cauchy sequences, generalized f-projection, continuity.
分类号 O177.2 [理学—基础数学]
  • 相关文献

参考文献17

  • 1Alber Ya. Metric and generalized projection operators in Banach spaces: Properties and applica- tions. Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type, Marcel Dekker, New York, 1996.
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  • 3刘英,佟慧.Banach空间中一类变分不等式的强收敛定理[J].系统科学与数学,2010,30(4):468-475. 被引量：2
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二级参考文献12

  • 1Alber Ya. Metric and generalized projection operators in Banach spaces: Properties and applications. Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type, Marcel Dekker, New York, 1996.
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  • 8Li J. On the existence of solutions of variational inequalities in Banach spaces. J. Math. Anal. Appl., 2004, 295:115-126.
  • 9Fan Jianghua. A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. J. Math. Anal. Appl., 2008, 337: 1041-1047.
  • 10Carlos M Y, Xu H K. Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 2006, 64: 2400-2411.

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系统科学与数学
2012年 第5期

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