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Publisher: Pergamon-elsevier Science LtdSubject: q-integers

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Now showing 1 - 3 of 3
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    Citation - WoS: 2
    Citation - Scopus: 2
    On the q-bernstein Polynomials of Piecewise Linear Functions in the Case q > 1
    (Pergamon-elsevier Science Ltd, 2013) Kaskaloglu, Kerem; Ostrovska, Sofiya
    The aim of this paper is to present new results related to the approximation of continuous functions by their q-Bernstein polynomials in the case q > 1. The first part of the paper is devoted to the behavior of the q-Bernstein polynomials of piecewise linear functions. This study naturally leads to the notion of truncated q-Bernstein polynomials introduced in the paper. The second part deals with the asymptotic estimates for the norms of the m-truncated q-Bernstein polynomials, in the case where both n and q vary. The results of the paper are illustrated by numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.
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    Citation - WoS: 5
    Citation - Scopus: 6
    The Norm Estimates of the q-bernstein Operators for Varying q > 1
    (Pergamon-elsevier Science Ltd, 2011) Ostrovska, Sofiya; Ozban, Ahmet Yasar
    The aim of this paper is to present norm estimates in C [0, 1] for the q-Bernstein basic polynomials and the q-Bernstein operators B-n,B-q in the case q > 1. While for 0 < q <= 1, vertical bar vertical bar B-n,B-q vertical bar vertical bar = 1 for all n is an element of N. in the case q > 1, the norm vertical bar vertical bar B-n,B-q vertical bar vertical bar increases rather rapidly as q -> +infinity. In this study, it is proved that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to C(n)q(n(n-1)/2), q -> +infinity with C-n = 2/n (1- 1/n)(n-1). Moreover, it is shown that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to 2q(n(n-1)/2) /ne as n -> infinity, q -> +infinity. The results of the paper are illustrated by numerical examples. (C) 2011 Elsevier Ltd. All rights reserved.
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    Citation - WoS: 8
    Citation - Scopus: 8
    On the Lupas q-transform
    (Pergamon-elsevier Science Ltd, 2011) Ostrovska, Sofiya
    The Lupas q-transform emerges in the study of the limit q-Lupas operator. The latter comes out naturally as a limit for a sequence of the Lupas q-analogues of the Bernstein operator. Lately, it has been studied by several authors from different perspectives in mathematical analysis and approximation theory. This operator is closely related to the q-deformed Poisson probability distribution, which is used widely in the q-boson operator calculus. (Lambda(q)f)(z) := 1/(-z; q)(infinity) . Sigma(infinity)(k=0) f(1 - q(k))q(k(k-1)/2)/(q; q)(k) z(k). In this paper, we study some analytic properties of (Lambda(q)f)(z). In particular, we examine the conditions under which Lambda(q)f can either be an entire function, or a rational one. (C) 2010 Elsevier Ltd. All rights reserved.