© Hindawi Publishing Corp. REMARKS ON A PAPER BY SILVERMAN

Abstract. We improve a result in Silverman’s paper (1999) and answer a question he posed. We also consider a similar problem and obtain sufficient conditions for starlikeness. 2000 Mathematics Subject Classification. 30C45. 1. Introduction. Let A be the class of analytic functions in the unit disc U = {z: |z|< 1} having expansion of the form f(z) = z+a2z2+a3z3+·· · (1.1) and let S ⊂ A be the set of univalent functions in U. A function f ∈ S is said to be starlike of order α, 0 < α < 1, and is denoted by S∗α if Rez(f ′(z)/f(z))> α, z ∈