论文信息 - Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi andW. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).

Yali Wang | Yinying Zhou | Jiantao Cao

[1] Gao Gai-liang. Weak Convergence Theorems for Nonexpansive Mappings , 2004 .

[2] Somyot Plubtieng,et al. A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces , 2007 .

[3] Chi Kin Chan,et al. A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization , 2009 .

[4] Wataru Takahashi,et al. Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings , 2003 .

[5] Shin Min Kang,et al. Approximation of common solutions of variational inequalities via strict pseudocontractions , 2012 .

[6] Jen-Chih Yao,et al. On modified iterative method for nonexpansive mappings and monotone mappings , 2007, Appl. Math. Comput..

[7] Gang Cai,et al. A hybrid approximation method for equilibrium and fixed point problems for a family of infinitely nonexpansive mappings and a monotone mapping , 2009 .

[8] Liu Min,et al. A new iterative method for finding common solutions of generalized equilibrium problem, fixed point problem of infinite k-strict pseudo-contractive mappings, and quasi-variational inclusion problem , 2012 .

[9] Wataru Takahashi,et al. Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem , 2007 .