Sharp Coefficient Bounds for a New Subclass of q-Starlike Functions Associated with q-Analogue of the Hyperbolic Tangent Function

In this study, by making the use of q-analogous of the hyperbolic tangent function and a Salagean q-differential operator, a new class of q-starlike functions is introduced. The prime contribution of this study covers the derivation of sharp coefficient bounds in open unit disk U, especially the first three coefficient bounds, Fekete-Szego type functional, and upper bounds of second- and third-order Hankel determinant for the functions to this class. We also use Zalcman and generalized Zalcman conjectures to investigate the coefficient bounds of a newly defined class of functions. Furthermore, some known corollaries are highlighted based on the unique choices of the involved parameters l and q.