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

Published:2007-09-01
Printed: Sep 2007
• M. Ali Õzarslan
• Oktay Duman
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Abstract

In the present paper, we introduce a modification of the Meyer-K\"{o}nig and Zeller (MKZ) operators which preserve the test functions $f_{0}(x)=1$ and $f_{2}(x)=x^{2}$, and we show that this modification provides a better estimation than the classical MKZ operators on the interval $[\frac{1}{2},1)$ 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.
 Keywords: Meyer-König and Zeller operators, Korovkin type approximation theorem, modulus of continuity, Lipschitz class functionals
 MSC Classifications: 41A25 - Rate of convergence, degree of approximation 41A36 - Approximation by positive operators

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