应用数学和力学（英文版）
應用數學和力學（英文版）
응용수학화역학（영문판）
APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION)
2010年
10期
1273-1282
,共10页
viscosity approximation%weak contraction mapping%equilibrium problem%nonexpansive mapping%implicit iteration%minimization problem
This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction. The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality. Under suitable conditions, some strong convergence theorems are established in the framework of Hilbert spaces. The results presented in the paper improve and extend the corresponding results of Colao et al. (Colao, V., Acedo, G. L., and Marino, G. An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings. Nonlinear Anal. 71,2708-2715(2009)), Plubtieng and Punpaeng (Plubtieng, S. And Punpaeng,R. A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces. J. Math. Anal. Appl. 336, 455-469 (2007)), Colao et al. (Colao, V., Marino, G., and Xu, H. K. An iterative method for finding common solutions of equilibrium problem Y., Liou, Y. C., and Yao, J. C. Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings. Fixed Point Theory Application2007, Article ID 64363 (2007) DOI 10.1155/2007/64363), and others.
