Geodesic
MKZ Type Operators Providing a Better Estimation on [1/2, 1)
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 434-439

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DOI

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.
DOI : 10.4153/CMB-2007-042-8
Mots-clés : 41A25, 41A36, Meyer-König and Zeller operators, Korovkin type approximation theorem, modulus of continuity, Lipschitz class functionals 
Özarslan, M. Ali; Duman, Oktay. MKZ Type Operators Providing a Better Estimation on [1/2, 1). Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 434-439. doi: 10.4153/CMB-2007-042-8
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     title = {MKZ {Type} {Operators} {Providing} a {Better} {Estimation} on [1/2, 1)},
     journal = {Canadian mathematical bulletin},
     pages = {434--439},
     year = {2007},
     volume = {50},
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     doi = {10.4153/CMB-2007-042-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-042-8/}
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