可数簇全拟- Φ -渐近非扩张映象和广义混合平衡问题以及极大单调算子的收缩投影迭代算法

Abstract

Abstract:

The purpose of this paper is first to introduce the concept of total quasi-Φ-asympto- tically nonexpansive mapping and then consider a hybrid shrinking projection method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem, the set ∩^∞_i=1F(S_i) of common fixed points of a countable family of total quasi-Φ-asymptotically nonexpansive mappings {S_i}^∞_i=1 and the set T^-10 of zeros of a maximal monotone operator T in a
uniformly smooth and strictly convex Banach space with Kadec-Klee property. It is proven that under appropriate conditions, the sequence generated by the hybrid shrinking projection method, converges strongly to some point in GMEP ∩T^-10 ∩(∩^∞_i=1F(S_i)). This new result represents the improvement, complement and development of the previously known ones in the literature.

Key words: Generalized mixed equilibrium problem, Total quasi-Φ-asymptotically nonexpansive mapping, Quasi-Φ-asymptotically nonexpansive mapping, Quasi-Φ-nonexpansive mapping, Hybrid shrinking projection, β-Inverse strongly monotone mapping, Maximal monotone operator

CLC Number:

47H06

ZHU Jin-Hua. Hybrid Shrinking Projection Method for a Countable Family of Total Quasi-Φ-Asymptotically Nonexpansive Mappings, a Generalized Mixed Equilibrium Problem and a Maximal Monotone Operator[J].Acta mathematica scientia,Series A, 2014, 34(2): 283-302.

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Hybrid Shrinking Projection Method for a Countable Family of Total Quasi-Φ-Asymptotically Nonexpansive Mappings, a Generalized Mixed Equilibrium Problem and a Maximal Monotone Operator

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