On Coefficient Inequalities of Starlike Functions Related to the q-Analog of Cosine Functions Defined by the Fractional q-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.

Third Hankel Determinant for Subclasses of Analytic and m-Fold Symmetric Functions Involving Cardioid Domain and Sine Function

“…Examples regarding the sharp bounds of the third Hankel determinant for particular subclasses of starlike functions, a number of recent developments from the year 2023 are mentioned in [38] and the references therein.…”