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

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 fm(x)=(1−x)−m are computed explicitly. From this we also derive a quite simple representation in terms of the functions hm(x)=xm/(1−x)m.