Weak Convergence of Iterative Approximation for Fixed Points of A Monotone α-nonexpansive Mapping

2019 2nd International Conference on Advanced Materials, Intelligent Manufacturing and Automation

Zhang, Rong^1

School of Science, Chongqing University of Posts and Telecommunications, Chongqing

400065, China^1

关键词: Approximation methods;    Fixed points;    Iterative approximations;    Nonexpansive mappings;    Partial order;    Topic Classification;    Uniformly convex Banach space;    Weak convergence;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/569/5/052095/pdf
DOI  :  10.1088/1757-899X/569/5/052095

来源: IOP

【 摘 要 】

In this paper, a modified approximation method is introduced for finding the fixed point of α-nonexpansive mapping in a uniformly convex Banach space with a partial order. Moreover, the weak convergence theorems of the fixed point of α-nonexpansive mapping are established under Opial and weak-Opial conditions, respectively. Topic classification: 47H05; 47H09; 47H10 CLC number: O177.91 Document code: A.