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    On gauss-weierstrass type integral operators
    (Walter de Gruyter GmbH, 2010) Anastassiou G.A.; Aral A.
    In this paper, we introduce a generalization of Gauss-Weierstrass operators based on q-integers using the q-integral and we call them q-Gauss-Weierstrass integral operators. For these operators, we obtain a convergence property in a weighted function space using Korovkin theory. Then we estimate the rate of convergence of these operators in terms of a weighted modulus of continuity. We also prove optimal global smoothness preservation property of these operators. © 2010 Warsaw University. All rights reserved.