Strong convergence for asymptotical pseudocontractions with the demiclosedness principle in banach spaces

Fixexd point theory and applications

Yuan-Heng Wang¹  Yong-Hui Xia¹ 

[1] Department of Mathematics, Zhejiang Normal University, Zhejiang, China

关键词: demiclosedness principle;    generalized projection;    strong convergence;    asymptotically pseudo-contractions;    Banach space;   

DOI  :  10.1186/1687-1812-2012-45

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The aim of this article is to give an answer to an interesting question proposed in Zhou. At the end of his article, he remarked that it was of great interest to extend his results to certain Banach spaces. So in this article, we extend the demiclosedness principle from Hilbert spaces to Banach spaces. A strong convergence theorem for asymptotical pseudo-contractions in Banach spaces is established. The approaches are based on the extended demiclosedness principle, and the generalized projective operator, and the hybrid method in mathematical programming. Our results extend the previous known results from Hilbert spaces to Banach spaces. MSC: 47H10; 47H09; 47H05.

【 授权许可】

CC BY