scholarly journals Extended Newton-type Method for Generalized Equations with Hölderian Assumptions

2021 ◽  
pp. 1-13
Author(s):  
Most Zamilla KHATON ◽  
Mohammed Harunor RASHİD
Keyword(s):  
Generalized Equations ◽  
Type Method

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

2018 ◽  
Vol 10 (4) ◽  
pp. 1
Author(s):  
M. Khaton ◽  
M. Rashid ◽  
M. Hossain
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Iteration Method ◽  
Generalized Equation ◽  
Generalized Equations ◽  
Convergence Properties ◽  
Closed Graph ◽  
Point Bar ◽  
Type Method ◽  
Set Valued Mapping

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.

scholarly journals On the Local Convergence of Regula-falsi-type Method for Generalized Equations

2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Farhana Alam ◽  
◽  
M. H. Rashid ◽  
M. A. Alom ◽  
◽  
...  
Keyword(s):  
Local Convergence ◽  
Generalized Equations ◽  
Type Method

scholarly journals Convergence of the Newton-Type Method for Generalized Equations

2016 ◽  
Vol 35 ◽  
pp. 27-40 ◽  
Author(s):  
MH Rashid ◽  
A Sarder
Keyword(s):  
Banach Spaces ◽  
Differentiable Function ◽  
Local Convergence ◽  
Generalized Equation ◽  
Generalized Equations ◽  
Closed Graph ◽  
Type Method ◽  
Set Valued Mapping ◽  
Fréchet Differentiable

Let X and Y be real or complex Banach spaces. Suppose that f: X->Y is a Frechet differentiable function and F: X => 2Yis a set-valued mapping with closed graph. In the present paper, we study the Newton-type method for solving generalized equation 0 ? f(x) + F(x). We prove the existence of the sequence generated by the Newton-type method and establish local convergence of the sequence generated by this method for generalized equation.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 27-40

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