Rate of approximation by $q$ -Durrmeyer operators in $L_{p}([0,1])$ , $1\leq p\leq\infty$

Abstract

We obtain global rates of approximation by q-Durrmeyer operators Dn,q(f;x) for the functions in the class Lp([0,1]),1≤p≤∞. First, rates of approximation in terms of the norms of f and f' and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness ωφ(f,δ).