New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators

被引：11

作者：

Su, Yongfu ^{[1
]}

Li, Mengqin ^{[1
]}

Zhang, Hong ^{[1
]}

机构：

[1] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 12期

关键词：

Hemi-relatively nonexpansive mapping; Generalized projection; Monotone hybrid algorithm; Cauchy sequence; Maximal monotone operator; STRONG-CONVERGENCE THEOREMS; ITERATIONS;

D O I：

10.1016/j.amc.2010.12.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this article is to prove the strong convergence theorems for hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems for hemi-relatively nonexpansive mappings, a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi-relatively nonexpansive mappings. Noting that, the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi-relatively nonexpansive mappings. However, this new monotone hybrid algorithm can be used for hemi-relatively nonexpansive mappings. In addition, a new method of proof has been used in this article. That is, by using this new monotone hybrid algorithm, we firstly claim that, the iterative sequence is a Cauchy sequence. The results of this paper modify and improve the results of Matsushita and Takahashi, and some others. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：5458 / 5465

页数：8

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