scholarly journals Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations

2013 ◽  
Vol 398 (1) ◽  
pp. 100-112 ◽  
Author(s):  
J.A. Ezquerro ◽  
M. Grau-Sánchez ◽  
M.A. Hernández ◽  
M. Noguera
Keyword(s):  
Semilocal Convergence ◽  
Operator Equations ◽  
Nondifferentiable Operator

scholarly journals Two-Step Solver for Nonlinear Equations

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 128 ◽  
Author(s):  
Ioannis Argyros ◽  
Stepan Shakhno ◽  
Halyna Yarmola
Keyword(s):  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Semilocal Convergence ◽  
Numerical Example ◽  
Weaker Conditions ◽  
Theoretical Results ◽  
Nondifferentiable Operator

In this paper we present a two-step solver for nonlinear equations with a nondifferentiable operator. This method is based on two methods of order of convergence 1 + 2 . We study the local and a semilocal convergence using weaker conditions in order to extend the applicability of the solver. Finally, we present the numerical example that confirms the theoretical results.

scholarly journals A Third Order Newton-Like Method and Its Applications

2018 ◽  
Author(s):  
D. R. Sahu ◽  
R. P. Agarwal ◽  
Y. J. Cho ◽  
V. K. Singh
Keyword(s):  
Nonlinear Operator ◽  
Lipschitz Continuity ◽  
Semilocal Convergence ◽  
Continuity Condition ◽  
Fredholm Integral Equations ◽  
Third Order ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
First Derivative ◽  
The Third

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

Fixed points for operators with generalized Hölder derivative

2014 ◽  
Vol 07 (04) ◽  
pp. 1450053
Author(s):  
I. K. Argyros ◽  
S. K. Khattri
Keyword(s):  
Fixed Points ◽  
Nonlinear Operator ◽  
Computational Cost ◽  
Semilocal Convergence ◽  
Convergence Criteria ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Numerical Examples

We present semilocal convergence criteria for approximating fixed points of nonlinear operator equations — with generalized Hölder derivative — by Newton-like methods. The new results extend the applicability of Newton-like methods in cases not covered in earlier studies. These results are obtained without additional computational cost. Numerical examples are presented where the new results improve the older results even when the same convergence criteria are used to justify convergence of these methods.

On Homogenization of Controlled Objects Described by Operator Equations of Hammerstein Type

2003 ◽  
Vol 35 (11) ◽  
pp. 19-27
Author(s):  
Victor N. Mizernyi ◽  
Peter I. Kogut ◽  
Tatyana N. Rudyanova
Keyword(s):  
Operator Equations
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