Strong Convergence Theorems for Variational Inequalities and Common Fixed-Point Problems Using Relaxed Mann Implicit Iteration Methods

被引：3

作者：

Ceng, Lu-Chuan ^{[1
]}

Shang, Meijuan ^{[2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 201416, Peoples R China

[2] Shijiazhuang Univ, Coll Sci, Shijiazhuang 266100, Hebei, Peoples R China

来源：

MATHEMATICS | 2019年 / 7卷 / 05期

基金：

中国国家自然科学基金;

关键词：

relaxed Mann implicit iteration; general variational inequalities; countable many uniformly Lipschitzian pseudocontractions; asymptotically nonexpansive mapping in the intermediate sense; banach space; 47H09; 47J20; 49M05; NONEXPANSIVE-MAPPINGS; EXTRAGRADIENT METHOD; ACCRETIVE-OPERATORS; WEAK-CONVERGENCE; ERGODIC THEOREM; FINITE FAMILY; ALGORITHMS; SYSTEMS; CONSTRAINTS; SEMIGROUPS;

D O I：

10.3390/math7050424

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a countable family of uniformly Lipschitzian pseudocontractive mappings. More convergence theorems are proved under some suitable weak condition in both 2-uniformly smooth and uniformly convex Banach spaces.

引用

页数：16

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