Bernstein Approximation Problem for Differentiable Functions and Quasi-Analytic Weights

Quasi-analytic Vectors and Quasi-analytic Functions

Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions

We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of dimensionality. We show that renorming the space of infinitely differentiable functions in a suitable way allows weakly tractable uniform approximation by using only func...

ON THE APPROXIMATION OF ANALYTIC FUNCTIONS BY THE q-BERNSTEIN POLYNOMIALS IN THE CASE

Abstract. Since for q > 1, the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f ∈ C[0, 1] and ...

Some Results on Bernstein-sato Polynomials for Parametric Analytic Functions

This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in the case of one function. We also make an extensive study of an example for which we give an expression of a generic (and under some conditions, a relative) B...

Approximation of B -continuous and B -differentiable functions by GBS operators of q -Bernstein–Schurer–Stancu type

Bǎrbosu and Muraru (2015) introduced the bivariate generalization of the q -Bernstein–Schurer–Stancu operators and constructed a GBS operator of q -Bernstein–Schurer–Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In...