On the q-Bernstein polynomials of rational functions with real poles

The paper aims to investigate the convergence of the q-Bernstein polynomials Bn,q(f;x) attached to rational functions in the case q>1. The problem reduces to that for the partial fractions (x−α)−j, j∈N. The already available results deal with cases, where either the pole α is simple or α≠q−m, m∈N...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of mathematical analysis and applications Ročník 413; číslo 2; s. 547 - 556
Hlavní autori: Ostrovska, Sofiya, Özban, Ahmet Yaşar
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 15.05.2014
Predmet:
Approximation of unbounded functions
Convergence
Multiple pole
q-Bernstein polynomial
q-Integer
Rational function
q-Bernstein polynomial
Multiple pole
Approximation of unbounded functions
q-Integer
Rational function
Convergence
ISSN:0022-247X, 1096-0813
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:The paper aims to investigate the convergence of the q-Bernstein polynomials Bn,q(f;x) attached to rational functions in the case q>1. The problem reduces to that for the partial fractions (x−α)−j, j∈N. The already available results deal with cases, where either the pole α is simple or α≠q−m, m∈N0. Consequently, the present work is focused on the polynomials Bn,q(f;x) for the functions of the form f(x)=(x−q−m)−j with j⩾2. For such functions, it is proved that the interval of convergence of {Bn,q(f;x)} depends not only on the location, but also on the multiplicity of the pole – a phenomenon which has not been considered previously.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2013.12.009