A Semilocal Convergence of a Secant–Type Method for Solving Generalized Equations

Positivity ◽  
2006 ◽  
Vol 10 (4) ◽  
pp. 693-700 ◽  
Author(s):  
Said Hilout ◽  
Alain Piétrus
Keyword(s):  
Semilocal Convergence ◽  
Generalized Equations ◽  
Type Method

scholarly journals Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces

2018 ◽  
Vol 330 ◽  
pp. 732-741 ◽  
Author(s):  
Abhimanyu Kumar ◽  
D.K. Gupta ◽  
Eulalia Martínez ◽  
Sukhjit Singh
Keyword(s):  
Banach Spaces ◽  
Semilocal Convergence ◽  
Type Method ◽  
Lipschitz Conditions

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

On a sixth-order Jarratt-type method in Banach spaces

2015 ◽  
Vol 08 (04) ◽  
pp. 1550065 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Spaces ◽  
Semilocal Convergence ◽  
Fréchet Derivative ◽  
Sixth Order ◽  
Convergence Conditions ◽  
Type Method ◽  
Frechet Derivative ◽  
The Third ◽  
Local Convergence Analysis ◽  
Jarratt Method

We present a local convergence analysis of a sixth-order Jarratt-type method in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies such as [X. Wang, J. Kou and C. Gu, Semilocal convergence of a sixth-order Jarratt method in Banach spaces, Numer. Algorithms 57 (2011) 441–456.] require hypotheses up to the third Fréchet-derivative. Numerical examples are also provided in this study.

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