Rate of approximation by q-Durrmeyer operators in Lp([0,1]), 1≤p≤∞

Abstract

We obtain global rates of approximation by $q$-Durrmeyer operators $D_{n,q}(f;x)$ for the functions in the class $L_p\left(\right[0,1\left]\right),1\le p\le \infty$. First, rates of approximation in terms of the norms of $f$ and $f\text{'}$ 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 ${\omega }_{\phi }(f,\delta )$.