Approximation of set-valued functions by single-valued one
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...
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.
Soient et . Il existe une application (non linéaire) normiquement continue de l’espace des opérateurs bornés de dans sur l’espace des opérateurs compacts (resp. faiblement compacts) de dans telle que coïncide avec la distance de au sous-espace formé des opérateurs compacts (resp. faiblement compacts). Pour un opérateur donné de dans on étudie les propriétés de l’ensemble (resp. ) des opérateurs compacts (resp. faiblement compacts) tel que pour tout de (resp. ) la quantité...
Sur certains sous-ensembles de , on caractérise les fonctions de classe , les fonctions analytiques et des fonctions de type Gevrey, par leurs distances aux polynômes dans ou dans l’espace des fonctions continues.
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 (...).
We introduce modified -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 and compute the rate of convergence for the function belonging to the class .