Inertial Method for Solving Pseudomonotone Variational Inequality and Fixed Point Problems in Banach Spaces

被引：1

作者：

Maluleka, Rose ^{[1
,2
]}

Ugwunnadi, Godwin Chidi ^{[1
,3
]}

Aphane, Maggie ^{[1
]}

机构：

[1] Sefako Makgatho Hlth Sci Univ, Dept Math & Appl Math, POB 94, ZA-0204 Pretoria, South Africa

[2] Tshwane Univ Technol, Dept Math & Stat, Staatsartillerie Rd, ZA-0183 Pretoria, South Africa

[3] Univ Eswatini, Fac Sci & Engn, Dept Math, Private Bag 4,M201, Kwaluseni, Eswatini

来源：

AXIOMS | 2023年 / 12卷 / 10期

关键词：

Bregman distance; quasi-Bregman nonexpansive mapping; fixed point problem; subgradient and extragrdient method; inertial term; pseudomonotone operator; variational inequality problem; SUBGRADIENT EXTRAGRADIENT METHOD; STRONG-CONVERGENCE THEOREMS; NONEXPANSIVE-MAPPINGS; EXISTENCE; OPERATORS;

D O I：

10.3390/axioms12100960

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a new iterative method that combines the inertial subgradient extragradient method and the modified Mann method for solving the pseudomonotone variational inequality problem and the fixed point of quasi-Bregman nonexpansive mapping in p-uniformly convex and uniformly smooth real Banach spaces. Under some standard assumptions imposed on cost operators, we prove a strong convergence theorem for our proposed method. Finally, we perform numerical experiments to validate the efficiency of our proposed method.

引用

页数：21

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