CONVERGENCE THEOREMS OF MONOTONE $(\ALPHA, \BETA)$-NONEXPANSIVE MAPPINGS FOR NORMAL-S ITERATION IN ORDERED BANACH SPACES WITH CONVERGENCE ANALYSIS

KHANITIN  MUANGCHOO-IN; POOM KUMAM; JEN-CHIH  YAO; CHING-FENG WEN

CONVERGENCE THEOREMS OF MONOTONE $(\ALPHA, \BETA)$-NONEXPANSIVE MAPPINGS FOR NORMAL-S ITERATION IN ORDERED BANACH SPACES WITH CONVERGENCE ANALYSIS

Authors

KHANITIN MUANGCHOO-IN King Mongkut's University of Technology Thonburi (KMUTT). Bangkok, Thailand.
POOM KUMAM KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, KMUTT, Bangkok 10140, Thailand http://orcid.org/0000-0002-5463-4581
JEN-CHIH YAO Research Center for Interneural Computing, China Medical University Hospital China Medical University, Taichung, 40402, Taiwan
CHING-FENG WEN Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, 100, Shih-Chuan 1st Road, Kaohsiung, 80708, Taiwan

Keywords:

Ordered Banach space, fixed point, monotone $(\alpha, \beta)$-nonexpansive mapping, normal S-iteration

Abstract

In this work, we prove some theorems of existence of fixed points for a monotone $(\alpha, \beta)$-nonexpansive mapping in a uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of normal-S iteration under some control condition. Finally, we give two numerical examples to illustrate the main result in this paper.