<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In the present paper, we study a Kantorovich type generalization of Meyer-König and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0;A] ; 0 &lt; A &lt; 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them. </p></abstract>

In the present paper, we study a Kantorovich type generalization of Meyer-König and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0;A] ; 0 < A < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them.

Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions

Kirikkale University Faculty of Sciences and Arts, Department of Mathematics, Kirikkale-TURKEY

Gazi University Faculty of Sciences, Department of Mathematics, Ankara-TURKEY

Ankara University Faculty of Sciences, Department of Mathematics Ankara-TURKEY

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

In the present paper, we study a Kantorovich type generalization of Meyer-König and Zeller type operators via generating functions. Using Korovkin type theorem...

Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions

Published Online: Mar 05, 2014

Page range: 209 - 222

DOI: https://doi.org/10.2478/auom-2013-0053

Keywords
Positive Linear operators,Kantorovich-type operators, Meyer-Konig and Zeller operators, Modulus of contiunity, Modified Lipschitz class, r-th order generalization

This content is open access.

Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions

Published Online: Mar 05, 2014

Page range: 209 - 222

DOI: https://doi.org/10.2478/auom-2013-0053

KeywordsPositive Linear operators,Kantorovich-type operators, Meyer-Konig and Zeller operators, Modulus of contiunity, Modified Lipschitz class, r-th order generalization

This content is open access.

Keywords
Positive Linear operators,Kantorovich-type operators, Meyer-Konig and Zeller operators, Modulus of contiunity, Modified Lipschitz class, r-th order generalization