### A Characterization of C(X) Among Algebras on Planar Sets by the Existence of a Finite Universal Korovkin System.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

2000 Mathematics Subject Classification: 41A25, 41A36.The purpose of this paper is to present a characterization of a certain Peetre K-functional in Lp[−1,1] norm, for 1 ≤ p ≤ 2 by means of a modulus of smoothness. This modulus is based on the classical one taken on a certain linear transform of the function.

Using the concept of $\mathcal{I}$-convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.

One of the Bernstein theorems that the class of bounded functions of the exponential type is dense in the space of bounded and uniformly continuous functions. This theorem follows from a convergence theorem for some interpolating operators on the real axis.

In this paper we study approximation properties of partial modified Szasz-Mirakyan operators for functions from exponential weight spaces. We present some direct theorems giving the degree of approximation for these operators. The considered version of Szász-Mirakyan operators is more useful from the computational point of view.

We prove that, for a sequence of positive numbers δ(n), if ${n}^{1/2}\delta \left(n\right)\neg \to \infty $ as $n\to \infty $, to guarantee that the modified Szász-Mirakjan operators ${S}_{n,\delta}(f,x)$ converge to f(x) at every point, f must be identically zero.

We prove a local saturation theorem in ordinary approximation for combinations of Durrmeyer's integral modification of Bernstein polynomials.