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October 2019 Some properties of q-Bernstein-Durrmeyer operators
Harun Karsli
Tbilisi Math. J. 12(4): 189-204 (October 2019). DOI: 10.32513/tbilisi/1578020576

Abstract

In the present paper we shall investigate the pointwise approximation properties of the q analogue of the Bernstein-Durrmeyer operators and estimate the rate of pointwise convergence of these operators to the functions $f$ whose q-derivatives are bounded variation on the interval $[0,1]$. We give an estimate for the rate of convergence of the operator $\left( L_{n,q}f \right)$ at those points $x$ at which the one sided q-derivatives $ D_{q}^{+}f(x),D_{q}^{-} f(x)$ exist. We shall also prove that the operators $L_{n,q}f$ converges to the limit $f(x).$ To the best of my knowledge, the present study will be the first study on the approximation of q- operators in the space of $D_{q}BV$.

Citation

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Harun Karsli. "Some properties of q-Bernstein-Durrmeyer operators." Tbilisi Math. J. 12 (4) 189 - 204, October 2019. https://doi.org/10.32513/tbilisi/1578020576

Information

Received: 31 March 2019; Accepted: 12 November 2019; Published: October 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07179180
MathSciNet: MR4047584
Digital Object Identifier: 10.32513/tbilisi/1578020576

Subjects:
Primary: 41A25
Secondary: 41A35

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 4 • October 2019
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