Eigenfunctions of Durrmeyer-type modifications of Meyer–König and Zeller operators

Abstract

In this paper we consider a generalization of different variants of Durrmeyer-type modifications of Meyer–König and Zeller operators. Eigenfunctions in terms of linear combinations of the functions f m ( x)=(1− x) − m are computed explicitly. From this we also derive a quite simple representation in terms of the functions h m ( x)= x m /(1− x) m .