The Cauchy problem for the nonlinear Schrödinger Equation in H1.
The comparison of the convergence speed between Picard, Mann, Krasnoselskij and Ishikawa iterations in Banach spaces.
The convergence of an implicit mean value iteration.
The convergence of mean value iteration for a family of maps.
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 -stabilities of the Krasnoselskij and the Mann iterations.
The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous -strongly accretive operators in uniformly smooth Banach spaces.
The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions.
The equivalence between the -stabilities of Picard–Banach and Mann–Ishikawa iterations.
The equivalence of Mann iteration and Ishikawa iteration for -uniformly pseudocontractive or -uniformly accretive maps.
The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators.
The general hybrid approximation methods for nonexpansive mappings in Banach spaces.
The interaction of linear boundary value and nonlinear functional conditions
The existence of solutions is studied for certain nonlinear differential equations with both linear and nonlinear conditions
The iterative method of generalized -concave operators.
The Lagrange multipliers theorem for locally convex metric spaces
The large deformation of nonlinearly elastic shells in axisymmetric flows
The Newton-kantorovich Method under Mild Differentiability Conditions and the Patak Error Estimates.
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