The Kantorovich form of some extensions for the Szász-Mirakjan operators

Dan Bărbosu; Ovidiu T. Pop; Dan Miclăuş

doi:10.33993/jnaat391-916

Authors

Dan Bărbosu North University of Baia Mare, Romania
Ovidiu T. Pop National College "Mihai Eminescu", Satu Mare, Romania
Dan Miclăuş North University of Baia Mare, Romania

DOI:

https://doi.org/10.33993/jnaat391-916

Keywords:

Szász-Mirakjan operators, Kantorovich operators, Bohman-Korovkin theorem, modulus of continuity, Shisha-Mond theorem, degree of approximation, parametric extension, Korovkin theorem for the bivariate case, bivariate modulus of continuity

Abstract views: 268

Abstract

Recently, C. Mortici defined a class of linear and positive operators depending on a certain function \(\varphi\). These operators generalize the well known Szász-Mirakjan operators. A convergence theorem for the defined sequence by the mentioned operators was given.Other interesting approximation properties of these generalized Szász-Mirakjan operators and also their bivariate form were obtained by D. Bărbosu, O. T. Pop and D. Miclăuș.In the present paper we are dealing with the Kantorovich form of the generalized Szász-Mirakjan operators. We construct the Kantorovich associated operators and then we establish a convergence theorem for the defined operators. The degree of approximation is expressed in terms of the modulus of continuity. Next, we construct the bivariate and respectively the GBS corresponding operators and we establish some of their approximation properties.

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