Sublinear Convergence of the Chord Method at Singular Points.
Sufficient conditions for semilocal convergence of a fourth order multipoint iterative method for solving equations in Banach spaces.
Sufficient conditions for the convergence of iterations to points of attraction in Banach space.
Suites concordantes d'espaces normés et leurs applications I
Sur une méthode itérative de résolution de problèmes aux limites elliptiques non linéaires
Soit un opérateur non nécessairement linéaire d’un Hilbert de l’équation , pour donné dans . Nous étudions la convergence du schéma itératif suivant: aou est fonction d’un opérateur auto-adjoint choisi de telle sorte que l’inversion de soit immédiate numériquement. Par exemple avec un entier et une constante convenablement choisis. Nous appliquons les résultats à un problème aux limites non linéaires avec résultats numériques.
-stability of Picard iteration in metric spaces.
The Approximation of Generalized Turning Points by Projection Methods with Superconvergence to the Critical Parameter.
The column-updating method for solving nonlinear equations in Hilbert space
The comparison of the convergence speed between Picard, Mann, Krasnoselskij and Ishikawa iterations in Banach spaces.
The Dependence of Critical Parameter Bounds on the Monotonicity of a Newton Sequence.
The effect of rounding errors on a certain class of iterative methods
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover,...
The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions.
The finite element method for non-linear problems
The Newton-kantorovich Method under Mild Differentiability Conditions and the Patak Error Estimates.
The perturbed generalized proximal point algorithm
The Perturbed Generalized Tikhonov's Algorithm
We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.
The perturbed Tikhonov's algorithm and some of its applications
The rate of convergence of a modified Newton's process
The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics
The existence of a periodic solution of a nonlinear equation is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.
The Secant Method and Fixed Points of Nonlinear Operators.