The modified Mann type iterative algorithm for a countable family of totally quasi- ϕ -asymptotically nonexpansive mappings by the hybrid generalized f -projection method

Fixexd point theory and applications

Preedaporn Kanjanasamranwong²  Siwaporn Saewan²  Poom Kumam³  Yeol Je Cho⁴ 

[1] Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, Korea;Department of Mathematics and Statistics, Faculty of Science, Thaksin University (TSU), Pa Phayom, Thailand;Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, KMUTT, Bangmod, Thailand

关键词: generalized f-projection operator;    modified Mann type iterative sequence;    totally quasi-ϕ-asymptotically nonexpansive mapping;   

DOI  :  10.1186/1687-1812-2013-63

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this article is to introduce the modified Mann type iterative sequence, using a new technique, by the hybrid generalized f-projection operator for a countable family of totally quasi-ϕ-asymptotically nonexpansive mappings in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Then we prove that the modified Mann type iterative scheme converges strongly to a common element of the sets of fixed points of the given mappings. Our result extends and improves the results of Li et al. (Comput. Math. Appl. 60:1322-1331, 2010), Takahashi et al. (J. Math. Anal. Appl. 341:276-286, 2008) and many other authors. MSC:47H05, 47H09, 47H10.

【 授权许可】

CC BY