Convergence Analysis of a New Bregman Extragradient Method for Solving Fixed Point Problems and Variational Inequality Problems in Reflexive Banach Spaces

被引：0
作者：
Shaotao Hu
Yuanheng Wang
Qiao-Li Dong
机构：
[1] Chongqing Normal University,School of Marxism
[2] Chongqing,Department of Mathematics
[3] Zhejiang Normal University,College of Science
[4] Civil Aviation University of China,undefined
来源：
Journal of Scientific Computing | 2023年 / 96卷
关键词：
Fixed point; Modified extragradient method; Variational inequality; Pseudomonotone operator; Strong convergence; Reflexive Banach spaces; 47H05; 47J25; 47H10; 65J15; 65K15;
D O I：
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中图分类号：
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摘要：
We mainly introduce a new self-adaptive extragradient method by using the inertial technique for solving variational inequality problems of pseudomonotone operators and fixed point problems of Bregman relatively nonexpansive mappings in real reflexive Banach spaces. Precisely, we show that the sequence generated by our iterative process converges strongly to a common element for the solution set of variational inequality problems and the set of fixed points of Bregman relatively nonexpansive mappings. Additionally, some numerical examples are given to show the effectiveness of our algorithm. The results obtained in this paper are the improvement and supplement of many recent ones in the field.
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