Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces

被引：0
作者：
Yan Tang
Ratthaprom Promkam
Prasit Cholamjiak
Pongsakorn Sunthrayuth
机构：
[1] Chongqing Technology and Business University,College of Mathematics and Statistics
[2] Rajamangala University of Technology Thanyaburi (RMUTT),Department of Mathematics and Computer Science, Faculty of Science and Technology
[3] University of Phayao,School of Science
[4] Rajamangala University of Technology Thanyaburi (RMUTT),Department of Mathematics and Computer Science, Faculty of Science and Technology
来源：
Applications of Mathematics | 2022年 / 67卷
关键词：
maximal operator; Bregman distance; reflexive Banach space; weak convergence; strong convergence; 47H09; 47H10; 47J25; 47J05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed methods. The results presented in this paper improve and generalize many known results in recent literature.
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页码：129 / 152
页数：23
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