Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators

Abstract

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and K-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties.

Szász–Durrmeyer Operators Involving Confluent Appell Polynomials

“…can be obtained by considering this inequality in (6). If we choose δ = δ η (x), we can obtain the desired result.…”

“…Recently, they have remarkable studies in operator theory [6][7][8][9], analytic function theory [10], and other fields [11,12]. Now, we define the Durrmeyer-type generalization of Szász operators involving confluent Appell polynomials…”