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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^(v) _k (x) of variance v and Gould-Hopper polynomials are given.

Mathematics Subject Classification (2010): 41A25, 41A36, 33C45.

Keywords: Szasz-Durrmeyer operator, modulus of continuity, Brenke type polynomials, Gould-Hopper polynomials, Hermite polynomials.