On Durrmeyer Type Operator Linking Bernoulli Polynomials

Abstract

In this article, we capture a new Durrmeyer type operator, linking adjoint Bernoulli polynomials with the Baskakov basis functions. We estimate its moments and central moments and provide approximation results which include Korovkin-type estimate in weighted space. Additionally, we present a graphical interpretation of the operators applied to certain functions, quantitative Voronovskaja’s theorem in weighted space, and a theorem involving Peetre’s K-functional. Furthermore, we give theorems based on difference of operators.