Bernstein durrmeyer operators based on two parameters

Abstract

In the present paper, we study the applications of the extension of quantum calculus based on two parameters. We define beta function and establish an identity with gamma function, for two parameters (p, q), ie. the post-quantum calculus. We also propose the (p, q)-Durrmeyer operators, estimate moments and establish some direct results. Depending on the selection of p and q, the rate of convergence of the our new operators can provide better approximation than those of the Bernstein-Durrmeyer operators and its q-analogue. In the end, we provide some graphs using the software Mathematica.