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Nonlinear Fredholm integral equations and majorant functions
From the majorant principle of Kantorovich and the theoretical significance of Newton’s method, we obtain domains of existence and uniqueness of...
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An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh
The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple...
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New inertial algorithm for a class of equilibrium problems
The article introduces a new algorithm for solving a class of equilibrium problems involving strongly pseudomonotone bifunctions with a...
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Backward step control for Hilbert space problems
We analyze backward step control globalization for finding zeros of Gâteaux-differentiable functions that map from a Banach space to a Hilbert space....
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Polyak’s gradient method for split feasibility problem constrained by level sets
In this paper, we are concerned with the split feasibility problem (SFP) whenever the convex sets involved are composed of level sets. By applying...
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Convergence analysis of a new algorithm for strongly pseudomontone equilibrium problems
The paper introduces and analyzes the convergence of a new iterative algorithm for approximating solutions of equilibrium problems involving strongly...
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On the convergence of CQ algorithm with variable steps for the split equality problem
We investigate CQ algorithm for the split equality problem in Hilbert spaces. In such an algorithm, the selection of the step requires prior...
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On the convergence of Newton-like methods using restricted domains
We present a new semi-local convergence analysis for Newton-like methods in order to approximate a locally unique solution of a nonlinear equation...
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Convergence of Steffensen’s method for non-differentiable operators
We present a semilocal as well as a local convergence analysis of Steffensen’s method in order to approximate a locally unique solution of a...
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Semilocal convergence of an eighth-order method in Banach spaces and its computational efficiency
The aim of this paper is to study the semilocal convergence of the eighth-order iterative method by using the recurrence relations for solving...
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An extension of a theorem by Wang for Smale’s α-theory and applications
We present an extension of a Theorem by Wang (see Math. Comp. 68 , 169–186
1999 ) for Smale’s α -theory [16 ,17 ] in order to approximate a locally... -
A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations
In this work, we develop a derivative free iterative method for the implementation of Lavrentiev regularization for approximately solving the...
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A Newton-like method for generalized operator equations in Banach spaces
In this paper, we are concerned with the semilocal convergence analysis of a Newton-like method discussed by Bartle (Amer Math Soc 6 : 827–831,
1955 )... -
An hybrid method that improves the accessibility of Steffensen’s method
Steffensen’s method is known for its fast speed of convergence and its difficulty in applying it in Banach spaces. From the analysis of the...
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Efficient application of nonlinear stationary operators in adaptive wavelet methods—the isotropic case
This paper deals with the efficient application of nonlinear operators in wavelet coordinates using a representation based on local polynomials. In...
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Estimating upper bounds on the limit points of majorizing sequences for Newton’s method
We present new sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of an equation in a Banach space...
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Parallel regularized Newton method for nonlinear ill-posed equations
We introduce a regularized Newton method coupled with the parallel splitting-up technique for solving nonlinear ill-posed equations with smooth...
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On the solution of systems of equations with constant rank derivatives
The famous for its simplicity and clarity Newton–Kantorovich hypothesis of Newton’s method has been used for a long time as the sufficient...
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On the convergence of Newton-type methods under mild differentiability conditions
We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Newton-type methods, under mild...