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A Nice Representation for a Link Between Baskakov- and Szász–Mirakjan–Durrmeyer Operators and Their Kantorovich Variants

  • Margareta HeilmannEmail author
  • Ioan Raşa
Article
  • 48 Downloads

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 for integer values of the linking parameter which leads to a simple proof of convexity properties for the linking operators. This also solves an open problem mentioned in Baumann et al. (Results Math. 69(3):297–315, 2016). Another open problem is presented at the end of the paper.

Keywords

Linking operators Baskakov–Durrmeyer type operators Kantorovich modifications of operators 

Mathematics Subject Classification

41A36 41A10 41A28 

Notes

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Authors and Affiliations

  1. 1.School of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany
  2. 2.Department of MathematicsTechnical UniversityCluj-NapocaRomania

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