Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

被引：12

作者：

Ceng, Lu-Chuan ^{[1
]}

Petrusel, Adrian ^{[2
]}

Wen, Ching-Feng ^{[3
,4
,5
]}

Yao, Jen-Chih ^{[6
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Babes Bolyai Univ, Dept Math, Cluj Napoca 400084, Romania

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80708, Taiwan

[4] Kaohsiung Med Univ, Res Ctr Nonliear Anal & Optimizat, Kaohsiung 80708, Taiwan

[5] Kaohsiung Med Univ Hosp, Dept Med Res, Kaohsiung 80708, Taiwan

[6] China Med Univ Hosp, Res Ctr Interneural Comp, Taichung 40402, Taiwan

来源：

MATHEMATICS | 2019年 / 7卷 / 09期

关键词：

inertial-like subgradient-like extragradient method with line-search process; pseudomonotone variational inequality problem; asymptotically nonexpansive mapping; strictly pseudocontractive mapping; sequentially weak continuity; STRONG-CONVERGENCE; ACCRETIVE-OPERATORS; NONLINEAR MAPPINGS; SPLIT FEASIBILITY; FINITE FAMILY; ZERO POINTS; SYSTEMS;

D O I：

10.3390/math7090860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish strong convergence results for solving the VIP and CFPP by utilizing an inertial-like gradient-like extragradient method with line-search process. Via suitable assumptions, it is shown that the sequences generated by such a method converge strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI).

引用

页数：19

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