扩展到无弱序列连续对偶映射Banach空间的关于变分包含与不动点问题的广义迭代算法

数学物理学报 ›› 2018, Vol. 38 ›› Issue (2): 244-263.

扩展到无弱序列连续对偶映射Banach空间的关于变分包含与不动点问题的广义迭代算法

刘英

河北大学数学与信息科学学院河北保定 071002

收稿日期:2016-03-05 修回日期:2017-10-16 出版日期:2018-04-26 发布日期:2018-04-26
作者简介:刘英,E-mail:ly_cyh2013@163.com
基金资助:
国家自然科学基金（11401157）

The General Iterative Algorithms for Variational Inclusions and Fixed Point Problems Extended to Banach Spaces Without the Weakly Sequentially Continuous Duality Mapping

Liu Ying

College of Mathematics and Information Science, Hebei University, Hebei Baoding 071002

Received:2016-03-05 Revised:2017-10-16 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the NSFC(11401157)

摘要/Abstract

摘要： 该文根据广义迭代算法在无弱序列连续对偶映射的q-一致光滑的Banach空间引进了一迭代序列来寻找两个集合的公共元素，这两个集合分别是包含两个H-增生映射的一类非线性变分包含组的解集和一无限族严格伪压缩映射的公共不动点集.该迭代序列得到的这一公共元素还是某一变分不等式的唯一解.该文提高和扩展了一些相关结果.

关键词: H-增生映射, 变分包含, 严格伪压缩映射, 逆强增生映射, Sunny非扩张收缩

Abstract: In this paper, we introduce an iterative scheme by the general iterative method for finding a common element of the set of solutions of a general system of nonlinear variational inclusions for two H-accretive mappings and the set of common fixed points of an infinite family of strictly pseudo-contractive mappings which solves some variational inequality in q-uniformly smooth Banach spaces without the weakly sequentially continuous duality mapping. Our results improve and extend the corresponding results announced by many others.

Key words: H-Accretive mapping, Variational inclusion, Strictly pseudo-contractive mapping, Inverse-strongly-accretive mapping, Sunny nonexpansive retraction

中图分类号:

O177.91

刘英. 扩展到无弱序列连续对偶映射Banach空间的关于变分包含与不动点问题的广义迭代算法[J]. 数学物理学报, 2018, 38(2): 244-263.

Liu Ying. The General Iterative Algorithms for Variational Inclusions and Fixed Point Problems Extended to Banach Spaces Without the Weakly Sequentially Continuous Duality Mapping[J]. Acta mathematica scientia,Series A, 2018, 38(2): 244-263.

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