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Approximation of solutions of nonlinear initial-value problems by B-spline functions

Krzysztof Wesołowski (2011)

Banach Center Publications

This note is motivated by [GGG], where an algorithm finding functions close to solutions of a given initial value-problem has been proposed (this algorithm has been recalled in Theorem 2.2). In this paper we present a commonly used definition and basic facts concerning B-spline functions and use them to improve the mentioned algorithm. This leads us to a better estimate of the Cauchy problem solution under some additional assumption on f appearing in the Cauchy problem. We also estimate the accuracy...

Approximation of the Stieltjes integral and applications in numerical integration

Pietro Cerone, Sever Silvestru Dragomir (2006)

Applications of Mathematics

Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.

Approximation par des opérateurs compacts ou faiblement compacts à valeurs dans C ( X )

Hicham Fakhoury (1977)

Annales de l'institut Fourier

Soient W = L ' ( μ ) et V = C ( X ) . Il existe une application (non linéaire) normiquement continue T P ( T ) de l’espace des opérateurs bornés de W dans V sur l’espace des opérateurs compacts (resp. faiblement compacts) de W dans V telle que T - P ( T ) coïncide avec la distance de T au sous-espace formé des opérateurs compacts (resp. faiblement compacts). Pour un opérateur donné T de W dans V on étudie les propriétés de l’ensemble K ( T ) (resp. F ( T ) ) des opérateurs compacts (resp. faiblement compacts) tel que pour tout R de K ( T ) (resp. K ( T ) ) la quantité...

Approximation polynomiale de fonctions C et analytiques

Salah Baouendi, Charles Goulaouic (1971)

Annales de l'institut Fourier

Sur certains sous-ensembles de R n , on caractérise les fonctions de classe C , les fonctions analytiques et des fonctions de type Gevrey, par leurs distances aux polynômes dans L p ou dans l’espace des fonctions continues.

Approximation problems in modular spaces of double sequences.

Aleksander Waszak (1990)

Publicacions Matemàtiques

Let X denote the space of all real, bounded double sequences, and let Φ, φ, Γ be φ-functions. Moreover, let Ψ be an increasing, continuous function for u ≥ 0 such that Ψ(0) = 0.In this paper we consider some spaces of double sequences provided with two-modular structure given by generalized variations and the translation operator (...).

Approximation properties for modified ( p , q ) -Bernstein-Durrmeyer operators

Mohammad Mursaleen, Ahmed A. H. Alabied (2018)

Mathematica Bohemica

We introduce modified ( p , q ) -Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators D n , p , q * and compute the rate of convergence for the function f belonging to the class Lip M ( γ ) .

Currently displaying 381 – 400 of 467