Univalent functions with univalent Gelfond-Leontev derivatives

Abstract

We investigate functions of the form f(z) = z/(1 + 5 0 0 Sne Onz")=2 + E n s O n e " that are analytic in the unitary circle U. Necessary and sufficient conditions in terms of {n}for a trinomial f and the bounds of br, 1 § n 5 4 for a particular form of_ in certain subclasses of univalent functions with univalent Gelfond- Leonter derivatives in U are determined.

Keywords

• univalent
• conver
• gelfond-leontev derivatives