On the q-Bernstein Polynomials of Unbounded Functions with q>1

Abstract EN

The aim of this paper is to present new results related to the q-Bernstein polynomials Bn,q(f;x) of unbounded functions in the case q>1 and to illustrate those results using numerical examples.

As a model, the behavior of polynomials Bn,q(f;x) is examined both theoretically and numerically in detail for functions on [0,1] satisfying f(x)~Kx−α as x→0+, where α>0 and K≠0 are real numbers.