A new generalization of Szasz-Kantorovich operators on weighted space

Year 2022, Volume: 7 Issue: 2, 85 - 106, 30.09.2022

Harun Çiçek , Shaymaa Jameel Zainalabdin , Aydın İzgi

Abstract

The purpose of this article is to define a new generalization of Szász-Kantorovich operators. First, by using the Korovkin theorem on the new operator we define, its convergence properties and rates are examined. Then, the Voronovskaja-type theorem for the new operator is proven. Additionally, with the help of the modulus of continuity in the weighted space, rate of convergence the new operator is examined, and a theorem is proven for the operator we define by using functions that satisfy the Lipschitz condition. Finally, the convergence is demonstrated more clearly by numerical examples and plots.

Keywords

Linear positive operators, Szasz-­Kantorovich operators, ­Weighted space, Module of ­Continuity, Lipschitz class

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