Convergence Properties of Extended Newton-type Iteration Method for Generalized Equations

M. Khaton, M. Rashid and Md Saddam Hossain (emonhasannil@gmail.com)

Journal of Mathematics Research, 2018, vol. 10, issue 4, 1-18

Abstract: In this paper, we introduce and study the extended Newton-type method for solving generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\Omega\subseteq\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable in a neighborhood $\Omega$ of a point $\bar{x}$ in $\mathcal X$, $g:\Omega\subseteq \mathcal X\to \mathcal Y$ is linear and differentiable at a point $\bar{x}$, and $\mathcal F$ is a set-valued mapping with closed graph acting in Banach spaces $\mathcal X$ and $\mathcal Y$. Semilocal and local convergence of the extended Newton-type method are analyzed.

Keywords: Generalized equations; Semilocal convergence; Lipschitz--like mappings; Extended Newton-type method; Divided difference (search for similar items in EconPapers)
Date: 2018
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