Strong convergence of three-step iteration methods for a countable family of generalized strict pseudocontractions in Hilbert spaces

Fixexd point theory and applications

Xiao-Jie Wang¹  Shi-Xiu Li¹  Hui-Ying Hu¹  Lu-Chuan Ceng¹ 

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

关键词: generalized strict pseudocontraction;    uniformly Lipschitz;    uniformly closed;    strong convergence;    fixed point;   

DOI  :  10.1186/1687-1812-2014-66

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce a new class of generalized strict pseudocontractions in a real Hilbert space, and we consider a three-step Ishikawa-type iteration methodMathMLfor finding a common fixed point of a countable family MathML of uniformly Lipschitz generalized MathML-strict pseudocontractions. Under mild conditions imposed on the parameter sequences MathML, MathML and MathML, we prove the strong convergence of MathML to a common fixed point of a countable family MathML of uniformly Lipschitz generalized strict pseudocontractions. On the other hand, we also introduce three-step hybrid viscosity approximation method for finding a common fixed point of a countable family MathML of uniformly Lipschitz generalized MathML-strict pseudocontractions with MathML, i.e., a countable family MathML of uniformly Lipschitz pseudocontractions. Under appropriate conditions we derive the strong convergence results for this method. The results presented in this paper improve and extend the corresponding results in the earlier and recent literature.

【 授权许可】

CC BY