A Nice Representation for a Link between Baskakov- and Sz\'asz-Mirakjan-Durrmeyer Operators and their Kantorovich Variants

Abstract

In this paper we consider a link between Baskakov-Durrmeyer type operators and corresponding Kantorovich type modifications of their classical variants. We prove a useful representation for Kantorovich variants of arbitrary order which leads to a simple proof of convexity properties for the linking operators. This also solves an open problem. Another open problem is presented at the end of the paper.