Szász–Durrmeyer Operators Involving Confluent Appell Polynomials

Abstract

This article is concerned with the Durrmeyer-type generalization of Szász operators, including confluent Appell polynomials and their approximation properties. Also, the rate of convergence of the confluent Durrmeyer operators is found by using the modulus of continuity and Peetre’s K-functional. Then, we show that, under special choices of A(t), the newly constructed operators reduce confluent Hermite polynomials and confluent Bernoulli polynomials, respectively. Finally, we present a comparison of newly constructed operators with the Durrmeyer-type Szász operators graphically.