两个平衡问题和可数无穷多非扩张映像公共不动点问题的新的迭代算法

Abstract

Abstract:

Very recently, Hu C S and Cai G^[7] suggested and analyzed two iterative schemes for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for an infinite family of α_i-inverse-strongly monotone mappings in the framework of Hilbert space. In this paper, we introduce a new iterative scheme for finding a common element of the sets of solutions of two equilibrium problems for two infinite families of inverse-strongly monotone mappings and the set of common fixed points for a family of infinitely nonexpansive mappings in a Hilbert space. Then we prove some strong convergence theorems which extend and improve Hu Changsong and Cai Gang's results(2010).

Key words: Strong convergence, Equilibrium problem, Fixed point, Variational , inequality, Inverse-strongly monotone mapping

CLC Number:

47H09

HU Hui-Ying, ZENG Liu-Chuan. The New Iterative Scheme for two Equilibrium Problems and Fixed Point Problems of Infinitely Nonexpansive Mappings[J].Acta mathematica scientia,Series A, 2013, 33(5): 860-881.

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References

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The New Iterative Scheme for two Equilibrium Problems and Fixed Point Problems of Infinitely Nonexpansive Mappings

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