The Rate of Convergence of Lupas q -Analogue of the Bernstein Operators

Abstract

We discuss the rate of convergence of the Lupas $q$-analogues of the Bernstein operators $R_{n,q}(f;x)$ which were given by Lupas in 1987. We obtain the estimates for the rate of convergence of $R_{n,q}(f)$ by the modulus of continuity of $f$, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.