Coupling Ishikawa algorithms with hybrid techniques for pseudocontractive mappings

Fixexd point theory and applications

Yonghong Yao³  Mihai Postolache⁴  Yeong-Cheng Liou⁵ 

[1] of Bucharest, Bucharest, Romania;Department of Information Management, Cheng Shiu University, Kaohsiung, Taiwan;Department of Mathematics, Tianjin Polytechnic University, Tianjin, China;Faculty of Applied Sciences, University ‘Politehnica’

关键词: pseudocontractive mappings;    Ishikawa algorithm;    hybrid algorithms;    fixed point;    strong convergence;   

DOI  :  10.1186/1687-1812-2013-211

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

It is well-known that Mann’s algorithm fails to converge for Lipschitzian pseudocontractions and strong convergence of Ishikawa’s algorithm for Lipschitzian pseudocontractions have not been achieved without compactness assumption on pseudocontractive mapping T or underlying space C. A new algorithm, which couples Ishikawa algorithms with hybrid techniques for finding the fixed points of a Lipschitzian pseudocontractive mapping, is constructed in this paper. Strong convergence of the presented algorithm is shown without any compactness assumption. MSC:47H05, 47H10, 47H17.

【 授权许可】

CC BY