Modified block iterative procedure for solving the common solution of fixed point problems for two countable families of total quasi- ϕ -asymptotically nonexpansive mappings with applications

Fixexd point theory and applications

Pongrus Phuangphoo²  Poom Kumam³ 

[1] Department of Mathematics, Faculty of Education, Bansomdejchaopraya Rajabhat University (BSRU), Thonburi, Bangkok, Thailand;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Kru, Bangkok, Thailand

关键词: strong convergence theorem;    total quasi-ϕ-asymptotically nonexpansive mapping;    fixed point problems;   

DOI  :  10.1186/1687-1812-2012-198

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce a new iterative procedure which is constructed by the modified block hybrid projection method for solving a common solution of fixed point problems for two countable families of uniformly total quasi-ϕ-asymptotically nonexpansive and uniformly Lipschitz continuous mappings. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property. Finally, we apply the problem of a strong convergence theorem concerning maximal monotone operators in Banach spaces. MSC:47H09, 47H10, 47H20, 47J20.

【 授权许可】

CC BY