Shape-preserving properties of the limit q-Durrmeyer operator

Abstract

The present work aims to establish the shape-preserving properties of the limit q-Durrmeyer operator, Dq for 0<q<1. It has been proved that the operator is monotonicity- and convexity-preserving. What is more, it maps a function m-convex along {qj}j=0∞ to a function m-convex along any sequence {xqj}j=0∞, x∈(0,1).