Non-convex hybrid algorithm for a family of countable quasi-Lipschitz mappings and application

Fixexd point theory and applications

Pengcheng Ma¹  Yanxia Tang¹  Jinyu Guan¹  Yongchun Xu¹  Yongfu Su² 

[1] Department of Mathematics, Hebei North University, Zhangjiakou, China;Department of Mathematics, Tianjin Polytechnic University, Tianjin, China

关键词: nonexpansive mapping;    hybrid algorithm;    Cauchy sequence;    closed quasi-nonexpansive;    47H05;    47H09;    47H10;   

DOI  :  10.1186/s13663-015-0457-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this article is to establish a kind of non-convex hybrid iteration algorithms and to prove relevant strong convergence theorems of common fixed points for a uniformly closed asymptotically family of countable quasi-Lipschitz mappings in Hilbert spaces. Meanwhile, the main result is applied to get the common fixed points of finite family of quasi-asymptotically nonexpansive mappings. It is worth pointing out that a non-convex hybrid iteration algorithm is first presented in this article, a new technique is applied in our process of proof. Finally, an example is given which is a uniformly closed asymptotically family of countable quasi-Lipschitz mappings. The results presented in this article are interesting extensions of some current results.

【 授权许可】

CC BY