On subclasses of uniformly convex functions and corresponding class of starlike functions. (English) Zbl 0898.30010

Bharati, R.; Parvatham, R.; Swaminathan, A.

Tamkang J. Math. 28, No. 1, 17-32 (1997).

The authors consider functions \(f\) uniformly convex in the unit disk as introduced by A. W. Goodman [Ann. Pol. Math. 56, No. 1, 87-92 (1991; Zbl 0744.30010)] of the form \(f(z)= z-\sum^\infty_{k= 2} a_kz^k\), \(a_k\geq 0\). For these and related classes, they prove characterizations using the coefficients, distortion theorems and convolution results.

Reviewer: K.J.Wirths (Braunschweig)

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

uniformly convex functions; distortion theorems; convolution