Radius problems in the class S L*

Let S L* denote the class of all analytic functions f in the unit disc u with the normalization f(0) = f'(0) - 1 = 0 and satisfying the condition vertical bar[zf'(z)/f(z)](2) -1 vertical bar < 1; z is an element of u, thuszf'(z)/f(z) is in the interior of the right half of the lemniscate of Bernoulli (x(2) + y(2))(2)-(x(2) - y(2)) = 0. The relations between S L* and others classes geometrically defined are considered. The radii of alpha-convexity, of alpha-starlikeness (and some of others) of integral is an element of S L* are determined. (c) 2009 Elsevier Inc. All rights reserved.