A Radius Problem for a certain Class of Schlicht Functions

Abstract

In this work we apply a lemma of Tuan and Anh [5] to solve a radius problem for certain class of schlicht functions defined by a product of expressions having geometric meaning. Many interesting consequences of the result are derived for some well known classes of functions, most especially the novel radius of convexity of order 1/2 for functions of bounded turning in the unit disk |z|< 1.

Key words and phrases. Schlichtness, product combinations, radius problem, analytic and univalent functions.

2000 Mathematics Subject Classification. 30C45