A NEWTON-LIKE METHOD FOR SOLVING GENERALIZED OPERATOR EQUATIONS AND VARIATIONAL INEQUALITIES

被引：0

作者：

Sahu, D. R. ^{[1
]}

Singh, K. K. ^{[1
]}

Singh, V. K. ^{[1
]}

Cho, Y. J. ^{[2
,3
,4
]}

机构：

[1] Banaras Hindu Univ, Dept Math, Fac Sci, Varanasi 221005, Uttar Pradesh, India

[2] Gyeongsang Natl Univ, Dept Math Educ, Jinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea

[4] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2015年 / 16卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Monotone operators; Lipschitz operators; generalized operator equations; Frechet derivative; Newton-like method; semilocal convergence;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a semilocal convergence analysis of a Newton-like method for solving the generalized operator equations in Hilbert spaces and also discuss the convergence analysis of the proposed algorithm under weak conditions. We establish sharp generalizations of Kantorovich theory for operator equations when the derivative is not necessarily invertible. As a simple consequence of our result, we discuss the existence and uniqueness of solutions of mixed variational inequality problems. Finally, we give numerical examples for the equations involving single valued as well as multi-valued mappings.

引用

页码：217 / 229

页数：13

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