Strong convergence theorems for asymptotically nonexpansive nonself-mappings with applications

Fixexd point theory and applications

Afrah AN Abdou¹  Liaqat A Khan¹  Yeol Je Cho¹  Weiping Guo² 

[1] Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, P.R. China

关键词: asymptotically nonexpansive nonself-mapping;    strong convergence;    fixed point;    uniformly convex Banach space;   

DOI  :  10.1186/s13663-015-0463-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple iteration and prove some strong convergence theorems of the proposed iteration for an asymptotically nonexpansive nonself-mapping with the condition (BP). Finally, we give two examples to illustrate the main result in this paper. Our results improve and extend the corresponding results given by some authors.

【 授权许可】

CC BY