Anastassiou G.A.Aral A.2020-06-252020-06-25201004201213https://hdl.handle.net/20.500.12587/2128In 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.eninfo:eu-repo/semantics/closedAccessGauss-Weierstrass operatorsQ-derivativeQ-integralQexponential functionsWeighted approximationArticle4348418492-s2.0-85053136503Q1