Glasgow Mathematical Journal

Research Article

Coefficient conditions for starlike functions

S. Ruscheweyha1

a1 Math. Instttut d. Univ., D-8700 Würzburg, F.R.G.

Let {ak} be a sequence of non-negative real numbers satisfying a1 = l and

S0017089500006753_eqnU1

(1)

Brannan [1] proved that the function

S0017089500006753_eqnU2

(2)

is close-to-convex univalent in the unit disc D. The example

S0017089500006753_eqnU3

shows that the conclusion in Brannan's theorem is sharp in that sense that “close-to-convex” cannot be replaced by the stronger one: “starlike”. It is therefore of interest to see which additional condition can guarantee this stronger conclusion.

(Received March 02 1986)

Footnotes

Dept. Matemáticas, Universidad Tecnica F.S.M. Casilla 110-V, Valparaiso, Chile