A further refinement for coefficient estimates of univalent functions

Abstract

The coefficient inequalities of FitzGerald are used to show that if f ( z ) = z + a 2 z 2 + a 3 z 3 + … f(z) = z + {a_2}{z^2} + {a_3}{z^3} + \ldots is analytic and univalent in the unit disc, then | a n | > ( 1.0657 ) n |{a_n}| > (1.0657)n . The technique used to obtain this bound cannot yield a result better than | a n | > ( 1.0599 ) n |{a_n}| > (1.0599)n .