Certain Coefficient Problems for <i>q</i>-Starlike Functions Associated with <i>q</i>-Analogue of Sine Function

Abstract

This study introduces a subclass Sqs* of starlike functions associated with the q-analogue of the sine function defined in symmetric unit disk. This article comprises the investigation of sharp coefficient bounds, and the upper bound of the third-order Hankel determinant for this class. It also includes the findings of Zalcman and generalized Zalcman conjectures for functions of this class.

Keywords

• analytic functions
• <i>q</i>-starlike functions
• univalent function
• Hankel determinant
• symmetric matrix
• Zalcman inequalities