×

zbMATH — the first resource for mathematics

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

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
PDF BibTeX XML Cite