On gauss-weierstrass type integral operators
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.
Anastassiou, G., & Aral, A. (2010). On gauss-weierstrass type integral operators. Demonstratio Mathematica, 43 (4), 841-849. https://doi.org/10.1515/dema-2013-0268