The Approximation of Power Function by the <i>q</I>-bernstein Polynomials in the Case <i>q</I> &gt; 1

No Thumbnail Available

Date

2008

Authors

Ostrovska, Sofiya
Ostrovska, Sofiya

Journal Title

Journal ISSN

Volume Title

Publisher

Element

Open Access Color

OpenAIRE Downloads

OpenAIRE Views

Research Projects

Organizational Units

Journal Issue

Abstract

Since for q > 1. q-Bernstein polynomials 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. It is known that, in the case q > 1. the q-Bernstein polynomials approximate the entire functions and, in particular, polynomials uniformly on any compact set in C. In this paper. the possibility of the approximation for the function (z + a)(alpha), a >= 0. with a non-integer alpha > -1 is studied. It is proved that for a > 0, the function is uniformly approximated on any compact set in {z : vertical bar z vertical bar < a}, while on any Jordan arc in {z : vertical bar z vertical bar > a}. the uniform approximation is impossible, In the case a = 0(1) the results of the paper reveal the following interesting phenomenon: the power function z(alpha), alpha > 0: is approximated by its, q-Bernstein polynomials either on any (when alpha is an element of N) or no (when alpha is not an element of N) Jordan arc in C.

Description

Keywords

q-integers, q-binomial coefficients, q-Bernstein polynomials, uniform convergence

Turkish CoHE Thesis Center URL

Fields of Science

Citation

2

WoS Q

Q2

Scopus Q

Q2

Source

Volume

11

Issue

3

Start Page

585

End Page

597

Collections