Kernels for composition of positive linear operators

2025/06/30 by Ulrich Abel, Abel, Ulrich, Ana Maria Acu +5 · 1 citation
Mathematics · #Approximation Theory and Sequence Spaces #Holomorphic and Operator Theory #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2506.23579

Abstract

This paper investigates the composition of Bernstein--Durrmeyer operators and Szász--Mirakjan--Durrmeyer operators, focusing on the structure and properties of the associated kernel functions. In the case of the Bernstein--Durrmeyer operators, we establish new identities for the kernel arising from the composition of two and three operators, from which the commutativity of these operators follows naturally. Building on the eigenstructure of the Bernstein--Durrmeyer operator M_n, we obtain a representation of the iterate M_n^r as a linear combination of the operators M_k, for k=0,1,…,n. We also address the composition of Szász--Mirakjan--Durrmeyer operators and revisit a known result giving an elementary proof.

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• A representation for the integral kernel of the composition of multivariate Bernstein-Durrmeyer operators

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