On the rate of convergence for the q-Durrmeyer polynomials in complex domains

Abstract

The q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set 𝓓 ⊂ ℂ, the rate of convergence is O(qn ) as n → ∞. The sharpness of the obtained result is demonstrated.