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MKZ Type Operators Providing a Better Estimation on [1/2, 1)

Published online by Cambridge University Press:  20 November 2018

M. Ali Özarslan
Affiliation:
Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Mersin 10, Turkey e-mail: mehmetali.ozarslan@emu.edu.tr
Oktay Duman
Affiliation:
Department of Mathematics, TOBB University of Economics and Technology, Sögütözü 06530, Ankara, Turkey e-mail: oduman@etu.edu.tr
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Abstract

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In the present paper, we introduce a modification of the Meyer-König and Zeller $\left( \text{MKZ} \right)$ operators which preserve the test functions ${{f}_{0}}\left( x \right)=1$ and ${{f}_{2}}\left( x \right)={{x}^{2}}$, and we show that this modification provides a better estimation than the classical $\left( \text{MKZ} \right)$ operators on the interval $\left[ \frac{1}{2},1 \right)$ with respect to the modulus of continuity and the Lipschitz class functionals. Furthermore, we present the $r$-th order generalization of our operators and study their approximation properties.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2007

References

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