General iteration scheme for finding the common fixed points of an infinite family of nonexpansive mappings

Volume 9, Issue 11, pp 5720--5732
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Authors

Guangrong Wu - School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China. Liping Yang - School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China.

Abstract

The purpose of this paper is to suggest and analyze the general viscosity iteration scheme for an infinite family of nonexpansive mappings $\{T_i\}^\infty_{i=1}$. Additionally, it proves that this iterative scheme converges strongly to a common fixed point of $\{T_i\}^\infty_{i=1}$ in the framework of reflexive and smooth convex Banach space, which solves some variational inequality. Results proved in this paper improve and generalize recent known results in the literature.

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ISRP Style

Guangrong Wu, Liping Yang, General iteration scheme for finding the common fixed points of an infinite family of nonexpansive mappings, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 11, 5720--5732

AMA Style

Wu Guangrong, Yang Liping, General iteration scheme for finding the common fixed points of an infinite family of nonexpansive mappings. J. Nonlinear Sci. Appl. (2016); 9(11):5720--5732

Chicago/Turabian Style

Wu, Guangrong, Yang, Liping. "General iteration scheme for finding the common fixed points of an infinite family of nonexpansive mappings." Journal of Nonlinear Sciences and Applications, 9, no. 11 (2016): 5720--5732

Keywords

• Nonexpansive mapping
• general iteration scheme
• contraction
• smooth Banach space.

•  47H09
•  47H10
•  47J20

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