Coefficient Inequalities for <i>q</i>-Convex Functions with Respect to <i>q</i>-Analogue of the Exponential Function

Abstract

In mathematical analysis, the q-analogue of a function refers to a modified version of the function that is derived from q-series expansions. This paper is focused on the q-analogue of the exponential function and investigates a class of convex functions associated with it. The main objective is to derive precise inequalities that bound the coefficients of these convex functions. In this research, the initial coefficient bounds, Fekete–Szegő problem, second and third Hankel determinant have been determined. These coefficient bounds provide valuable information about the behavior and properties of the functions within the considered class.

Keywords

• analytic functions
• <i>q</i>-starlike functions
• <i>q</i>-convex functions
• Hankel determinants
• <i>q</i>-derivative operator
• subordination