Mann-type algorithms for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces

被引：7

作者：

Sunthrayuth, Pongsakorn ^{[1
]}

Pholasa, Nattawut ^{[2
]}

Cholamjiak, Prasit ^{[2
]}

机构：

[1] Rajamangala Univ Technol Thanyaburi RMUTT, Fac Sci & Technol, Dept Math & Comp Sci, Thanyaburi 12110, Pathumthani, Thailand

[2] Univ Phayao, Sch Sci, Phayao 56000, Thailand

来源：

RICERCHE DI MATEMATICA | 2023年 / 72卷 / 01期

关键词：

Maximal monotone operator; Banach space; Weak convergence; Fixed point problem; RELATIVELY NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE; ITERATIVE METHODS; WEAK-CONVERGENCE; SUM; THEOREMS;

D O I：

10.1007/s11587-021-00596-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce two algorithms for finding a common solution of the monotone inclusion problem and the fixed point problem for a relatively nonexpansive mapping in reflexive Banach spaces. The weak convergence results for both algorithms are established without the prior knowledge of the Lipschitz constant of the mapping. An application to the variational inequality problem is considered. Finally, some numerical experiments of the proposed algorithms including comparisons with other algorithms are provided.

引用

页码：63 / 90

页数：28

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