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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.)