# Accession Number:

## ADP013714

# Title:

## On the q-Bernstein Polynomials

# Descriptive Note:

## Conference paper

# Corporate Author:

## DOKUZ EYLUL UNIV IZMIR (TURKEY) DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 2001-07-01

# Pagination or Media Count:

## 7.0

# Abstract:

We discuss here recent developments on the convergence of the q-Bernstein polynomials Bsub nf which replaces the classical Bernstein polynomial with a one parameter family of polynomials. In addition, the convergence of iterates and iterated Boolean sum of q-Bernstein polynomial will be considered. Moreover a q-difference operator Dsub qf defined by Dsub qf fX,QX is applied to q-Bernstein polynomials. This gives us some results which complement those concerning derivatives of Bernstein polynomials. It is shown that, with the parameter 0 is less than q is less than or equal to 1, if the change in k, fsub r is greater than or equal to 0 then Dksub qBsub nf is greater than or equal to 0. If f is monotonic so is Dsub qBsub nf. If f is convex then D2sub qBsub nf is greater than or equal to 0.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Theoretical Mathematics