On a generalization of Szasz-Durrmeyer operators with some orthogonal polynomials

In this paper, we construct a form of linear positive operators with Brenke type polynomials as a generalization of Szasz-Durrmeyer operators. We obtain convergence properties of our operators with the help of the universal Korovkin-type property and calculate the order of approximation by using classical modulus of continuity. Explicit examples of our operators involving some orthonogal and d-orthogonal polynomials such as the Hermite polynomials H (ν) k (x) of variance ν and Gould-Hopper polynomials are given. Mathematics Subject Classification (2010): 41A25, 41A36, 33C45.