A <i>q</i>-Analog of the Class of Completely Convex Functions and Lidstone Series

Abstract

This paper introduces a q-analog of the class of completely convex functions. We prove specific properties, including that q-completely convex functions have convergent q-Lidstone series expansions. We also provide a sufficient and necessary condition for a real function to have an absolutely convergent q-Lidstone series expansion.

Keywords

• quantum calculus
• <i>q</i>-series
• <i>q</i>-Lidstone polynomials
• completely convex functions