Steepest-Descent Ishikawa Iterative Methods for a Class of Variational Inequalities in Banach Spaces

被引：3

作者：

Nguyen Buong ^{[1
,2
]}

Nguyen Quynh Anh ^{[3
]}

Khuat Thi Binh ^{[4
,5
]}

机构：

[1] Duy Tan Univ, 3 Quang Trung, Da Nang, Vietnam

[2] Vietnam Acad Sci & Technol, Inst Informat Technol, 18 Hoang Quoc Viet, Hanoi, Vietnam

[3] Peoples Police Univ Technol & Logist, Thuan Thanh, Bac Ninh, Vietnam

[4] Grad Univ Sci & Technol, 18 Hoang Quoc Viet, Hanoi, Vietnam

[5] Banking Acad, Hanoi, Vietnam

来源：

FILOMAT | 2020年 / 34卷 / 05期

关键词：

Nonexpansive mapping; fixed point; Variational inequality; NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE; FIXED-POINTS; ALGORITHM; APPROXIMATION; THEOREMS; EXAMPLE; FAMILY;

D O I：

10.2298/FIL2005557B

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, for finding a fixed point of a nonexpansive mapping in either uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly Gateaux differentiable norm, we present a new explicit iterative method, based on a combination of the steepest-descent method with the Ishikawa iterative one. We also show its several particular cases one of which is the composite Halpern iterative method in literature. The explicit iterative method is also extended to the case of infinite family of nonexpansive mappings. Numerical experiments are given for illustration.

引用

页码：1557 / 1569

页数：13

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