Strong convergence theorems for nonlinear operator equations with total quasi- ϕ -asymptotically nonexpansive mappings and applications

Fixexd point theory and applications

Shih-sen Chang¹  Lin Wang¹  Yong-Kun Tang¹  Yu Guang Xu²  Xiong-rui Wang³ 

[1] College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, China;Department of Mathematics, Kunming University, Kunming, Yunnan, China;Department of Mathematics, Yibin University, Yibin, Sichuan, China

关键词: total quasi-ϕ-asymptotically nonexpansive mappings;    generalized mixed equilibrium problems;    quasi-ϕ-asymptotically nonexpansive mappings;    relatively nonexpansive mapping;    variational inequalities;    Hammerstian type equation;    fixed point;   

DOI  :  10.1186/1687-1812-2012-34

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this article is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases, and then by using the hybrid algorithm to introduce a new iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, the set of common fixed points of a countable family of total quasi-ϕ-asymptotically nonexpansive mappings and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. As an application, we shall utilize our results to study the iterative solutions of the nonlinear Hammerstian type equation. The results presented in the article improve and extend the corresponding results announced by some authors. AMS (MOS) subject classification: 47H06; 47H09; 47J05; 47J25.

【 授权许可】

CC BY