q-一致光滑、一致凸Banach空间中关于变分不等式问题和严格伪压缩映射的不动点问题的粘性迭代算法

数学物理学报 ›› 2016, Vol. 36 ›› Issue (4): 623-638.

q-一致光滑、一致凸Banach空间中关于变分不等式问题和严格伪压缩映射的不动点问题的粘性迭代算法

蔡钢¹, Yekini Shehu²

1. 重庆师范大学数学科学学院重庆 401331;
2. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

收稿日期:2015-10-13 修回日期:2016-04-15 出版日期:2016-08-26 发布日期:2016-08-26
通讯作者: 蔡钢 E-mail:caigang-aaaa@163.com
作者简介:Yekini Shehu,yekini.shehu@unn.edu.ng
基金资助:
国家自然科学基金（11171172，11401063）、高等学校博士学科点专项科研基金（20120002110044）、重庆市自然科学基金（cstc2014jcyjA00016）和重庆市教委科技项目基金（KJ1500314）资助

Viscosity Iterative Algorithm for Variational Inequality Problems and Fixed Point Problems of Strict Pseudo-Contractions in q-Uniformly Smooth and Uniformly Convex Banach Spaces

Cai Gang¹, Yekini Shehu²

1. School of Mathematics Science, Chongqing Normal University, Chongqing 401331;
2. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

Received:2015-10-13 Revised:2016-04-15 Online:2016-08-26 Published:2016-08-26
Supported by:
Supported by the NSFC(11171172,11401063),the Specialized Research Fund for the Doctoral Program of Higher Education(20120002110044),the Natural Science Foundation of Chongqing(cstc2014jcyjA00016) and the Technology Project of Chongqing Education Committee(KJ1500314)

摘要/Abstract

摘要：

该文在q-一致光滑，一致凸 Banach 空间中研究了关于广义压缩映射的粘性迭代算法，找到了关于两个逆强增生算子的变分不等式问题解集与无限个严格伪压缩映射的公共不动点集的公共元. 所得结果提高和推广了许多最近的相关结果.

关键词: 不动点, 变分不等式, 强收敛, 伪压缩映射, Banach 空间

Abstract:

The purpose of this paper is to investigate a viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for two inverse-strongly accretive mappings and the set of common fixed points for infinite strict pseudo-contractions in q-uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are proved under some appropriate conditions. The results obtained in this paper improve and extend many recent ones announced by many others in this literature.

Key words: Fixed point, Variational inequality, Strong convergence, Pseudocontraction, Banach space

中图分类号:

O177.91

蔡钢, Yekini Shehu. q-一致光滑、一致凸Banach空间中关于变分不等式问题和严格伪压缩映射的不动点问题的粘性迭代算法[J]. 数学物理学报, 2016, 36(4): 623-638.

Cai Gang, Yekini Shehu. Viscosity Iterative Algorithm for Variational Inequality Problems and Fixed Point Problems of Strict Pseudo-Contractions in q-Uniformly Smooth and Uniformly Convex Banach Spaces[J]. Acta mathematica scientia,Series A, 2016, 36(4): 623-638.

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