GCRIS :: Search

Search Results

Now showing 1 - 2 of 2

Citation - WoS: 7
Citation - Scopus: 7
On the q-bernstein Polynomials of Unbounded Functions With q > 1
(Hindawi Ltd, 2013) Ostrovska, Sofiya; Ozban, Ahmet Yasar
The aim of this paper is to present new results related to the q-Bernstein polynomials B-n,B-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 B-n,B-q (f;x) is examined both theoretically and numerically in detail for functions on [0, 1] satisfying f(x) similar to Kx(-alpha) as x -> 0(+), where alpha > 0 and K not equal 0 are real numbers.
Citation - WoS: 3
Citation - Scopus: 5
On the Sets of Convergence for Sequences of the q-bernstein Polynomials With q > 1
(Hindawi Publishing Corporation, 2012) Ostrovska, Sofiya; Ozban, Ahmet Yasar
The aim of this paper is to present new results related to the convergence of the sequence of the q-Bernstein polynomials {B-n,B-q(f x)} in the case q > 1, where f is a continuous function on [0,1]. It is shown that the polynomials converge to f uniformly on the time scale J(q) = {q(-j)}(j-0)(infinity) boolean OR {0}, and that this result is sharp in the sense that the sequence {B-n,B-q(f;x)}(n-1)(infinity) may be divergent for all x is an element of R \ J(q). Further the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper the results are illustrated by numerical examples.