On a certain subclass of strongly starlike functions

Let S*(α₁, α₂), where α₁, α₂ ∈ (0, 1], represent the class of functions f that are analytic in the open unit disk D, normalized by f (0) = f ' (0) − 1 = 0, and satisfying the following double-sided inequality:

−πα₁ / 2 < arg {zf ' (z) / f (z)} < πα₂ / 2 , (z ∈ D).

In this manuscript, we estimate the coefficients and logarithmic coefficients associated with functions that belong to the class S*(α₁, α₂). As a result, we provide a general bound for the coefficients of a strongly starlike function, which has been an open question until now. Finally, we derive upper and lower bounds for the expression Re{zf '(z) / f (z)}, where f ∈ S*(α₁, α₂).