On Coefficient Inequalities of Starlike Functions Related to the <i>q</i>-Analog of Cosine Functions Defined by the Fractional <i>q</i>-Differential Operator

Abstract

This article extends the study of q-versions of analytic functions by introducing and studying the association of starlike functions with trigonometric cosine functions, both defined in their q-versions. Certain coefficient inequalities like coefficient bounds, Zalcman inequalities, and both Hankel and Toeplitz determinants for the new version of starlike functions are investigated. It is worth mentioning that most of the determined inequalities are sharp with the support of relevant extremal functions.

Keywords

• analytic function
• <i>q</i>-derivative (or difference) operator
• factorial functional
• exponential function
• univalent function
• <i>q</i>-starlike functions