On the $q$-Bernstein polynomials of the logarithmic function in the case $q>1$

Rok, strany: 2016, 73 - 78

The $q$-Bernstein basis used to construct the $q$-Bernstein polynomials is an extension of the Bernstein basis related to the $q$-binomial probability distribution. This distribution plays a profound role in the $q$-boson operator calculus. In the case $q>1$, $q$-Bernstein basic polynomials on $[0,1]$ combine the fast increase in magnitude with sign oscillations. This seriously complicates the study of $q$-Bernstein polynomials in the case of $q>1$. The aim of this paper is to present new results related to the $q$-Bernstein polynomials $B_n,q$ of discontinuous functions in the case $q>1$. The behavior of polynomials $B_n,q(f;x)$ for functions $f$ possessing a logarithmic singularity at $0$ has been examined.

ISO 690:

Ostrovska, S. 2016. On the $q$-Bernstein polynomials of the logarithmic function in the case $q>1$. In Mathematica Slovaca, vol. 66, no.1, pp. 73-78. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0116

APA:

Ostrovska, S. (2016). On the $q$-Bernstein polynomials of the logarithmic function in the case $q>1$. Mathematica Slovaca, 66(1), 73-78. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0116