Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov operators

Abstract

The modification of Bernstein operators given by Aldaz, Kounchev and Render has been intensively studied in the recent years. In this paper we define a corresponding modification for the general class of Baskakov-type operators. All these operators preserve the constants and j-th monomial for a given natural number j. We prove a general result of Voronovskaja type (Theorem 2.1) for positive linear operators acting on the infinite interval [0,?) and use this theorem to prove a Voronovskaja-type theorem for the whole class of the modified Baskakov-type operators.