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Now showing 1 - 3 of 3
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    Article
    Citation - WoS: 7
    On the Approximation of Analytic Functions by the q-bernstein Polynomials in the Case q > 1
    (Kent State University, 2010) Ostrovska, Sofiya
    Since for q > 1, the q-Bernstein polynomials B(n,q) are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f is an element of C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then B(n,q) (f; z) -> f (z) as n -> infinity, uniformly on any compact set in {z : |z| < a}.
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    Conference Object
    Citation - WoS: 1
    On Euler's differential methods for continued fractions
    (Kent State University, 2006) Khrushchev, Sergey; Mathematics
    A differential method discovered by Euler is justified and applied to give simple proofs to formulas relating important continued fractions with Laplace transforms. They include Stieltjes formulas and some Ramanujan formulas. A representation for the remainder of Leibniz's series as a continued fraction is given. We also recover the original Euler's proof for the continued fraction of hyperbolic cotangent.
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    Article
    Citation - Scopus: 7
    On the Approximation of Analytic Functions by the Q-Bernstein Polynomials in the Case Q > 1
    (Kent State University, 2010) Ostrovska,S.
    Since for q > 1, the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f Ε C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then Bn,q (f; z) → f(z) as n → λ, uniformly on any compact set in {z : |z| < a}. Copyright © 2010, Kent State University.