An extragradient-like approximation method for variational inequalities and fixed point problems

Fixexd point theory and applications

Jen-Chih Yao¹  Ngai-Ching Wong²  Lu-Chuan Ceng³  Qamrul Hasan Ansari⁴ 

[1] Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan;Department of Mathematics, Aligarh Muslim University, Aligarh, India;Department of Mathematics, Shanghai Normal University, Shanghai, China;Scientific Computing Key Laboratory Of Shanghai Universities, China

关键词: extragradient-like approximation method;    modified Mann iteration process;    variational inequality;    asymptotically strict pseudocontractive mapping in the intermediate sense;    fixed point;    monotone mapping;    strong convergence;    demiclosedness principle;   

DOI  :  10.1186/1687-1812-2011-22

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like approximation method and the modified Mann iteration process. We establish a strong convergence theorem for two sequences generated by this extragradient-like iterative algorithm. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings. 1991 MSC: 47H09; 47J20.

【 授权许可】

CC BY