Abstract

For a function $f(z)=z+a_2z^2+\dotsb$, analytic in the unit disc, we find $\lambda>0$ such that $|f''(z)|\le\lambda$ implies starlikeness (Mocanu's problem [2]) or convexity. The given results are sharp.

Keywords: Starlike, convex, subordinate.

MSC: 30C45

Pages:  241--244     

Volume  49 ,  Issue  3$-$4 ,  1997