Radius problems in the class [formula omitted

Abstract

Let SL ∗ 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 zf ′ ( z ) / f ( z ) 2 - 1 < 1 , z ∈ U , thus zf ′ ( z ) / f ( z ) is in the interior of the right half of the lemniscate of Bernoulli ( x 2 + y 2 ) 2 - 2 ( x 2 - y 2 ) = 0 . The relations between SL ∗ and others classes geometrically defined are considered. The radii of α -convexity, of α -starlikeness (and some of others) of f ∈ SL ∗ are determined.