A GENERAL COMPOSITE ITERATIVE METHOD FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS

被引：0

作者：

Jung, Jong Soo ^{[1
]}

机构：

[1] Dong A Univ, Dept Math, Pusan 604714, South Korea

来源：

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS | 2010年 / 12卷 / 01期

关键词：

Viscosity approximation method; Composite iterative scheme; Equilibrium problem; Fixed points; Variational inequality; Nonexpansive mapping; Contraction; VISCOSITY APPROXIMATION METHODS; STRONG-CONVERGENCE;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We introduce a new general composite iterative sheme by the viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert spaces. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping, which is the unique solution of a ceratin variational inquality. Our results substantially develop and improve the corresponding results of Jung [J. S. Jung, Strong convergence of composite iterative methods for equilibrium problems and fixed point problems in Hilber spaces, J. Math. Anal, Apple 336 (2007) 455-469], Shang et al. [M. Shang, X. Qin, Y. Sn, A general iterative method for equilibrium problems and fixed point problems, Fixed Point Theory Appl. (2007), Article ID 64306, 7 pages] and Takahashi and Takahashi [A. Takahashi and W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilber space, J. Math. Anal. appl. 333(2007) 506-515].

引用

页码：124 / 140

页数：17

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