On a certain subclass of strongly starlike functions

Abstract

Let S * t (α 1 , α 2 ) denote the class of functions f analytic in the open unit disc ∆, normalized by the condition f (0) = 0 = f ′ (0) − 1 and satisfying the following two-sided inequality:) is a subclass of strongly starlike functions of order β where β = max{α 1 , α 2 }. The object of the present paper is to derive some certain inequalities including (for example), upper and lower bounds for Re{zf ′ (z)/f (z)}, growth theorem, logarithmic coefficient estimates and coefficient estimates for functions f belonging to the class S * t (α 1 , α 2 ).2010 Mathematics Subject Classification. 30C45.

Majorization problems for certain starlike functions associated with the exponential function

“…For a brief survey on these numbers, readers may refer to [4,3]. Also, for more details about some another subclasses of the starlike functions with various special cases of ϕ, see [10,9,11,13,14,19,20,21].…”