GEOMETRIC INEQUALITIES FOR SOLVING VARIATIONAL INEQUALITY PROBLEMS IN CERTAIN BANACH SPACES

被引：4

作者：

Adamu, A. ^{[1
,2
]}

Chidume, C. E. ^{[3
]}

Kitkuan, D. ^{[4
]}

Kumam, P. ^{[2
,5
]}

机构：

[1] Near East Univ, Operat Res Ctr Healthcare, Nicosia, Turkiye

[2] King Mongkuts Univ Technol Thonburi, Ctr Excellence Theoret & Computat Sci, Sci Lab Bldg,126 Pracha Uthit Rd, Bangkok, Thailand

[3] African Univ Sci & Technol, Math Inst, Abuja, Nigeria

[4] Rambhai Barni Rajabhat Univ, Fac Sci & Technol, Dept Math, Chanthaburi 22000, Thailand

[5] King Mongkuts Univ Technol Thonburi, Fac Sci, Dept Math, Fixed Point Res Lab,Fixed Point Theory & Applicat, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

来源：

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS | 2023年 / 7卷 / 02期

关键词：

Relatively nonexpansive mapping; Subgradient method; Variational inequality; STRONG-CONVERGENCE; PROJECTION METHOD; MAPPINGS; ALGORITHM;

D O I：

10.23952/jnva.7.2023.2.07

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop some new geometric inequalities in p-uniformly convex and uni-formly smooth real Banach spaces with p > 1. We use the inequalities as tools to obtain the strong convergence of the sequence generated by a subsgradient method to a solution that solves fixed point and variational inequality problems. Furthermore, the convergence theorem established can be applica-ble in, for example, Lp(& omega;), where & omega; C R is bounded set and lp(R) for p E (2, & INFIN;). Finally, numerical implementations of the proposed method in the real Banach space L5([-1,1]) are presented.

引用

页码：267 / 278

页数：12

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