Univalent functions with missing Taylor coefficients

For n ≥ 2, let U(λ) denote the class of all analytic functions f in the unit disc Δ of the form f(z) = z + an + 1zn + 1+… satisfying the condition f’(z) = z2/f(z)-1 < λ z ϵ Δ. In this paper, among other results, we find condition on < so that each function in U(λ) is starlike, strongly starlike or convex of some order. In addition, we discuss the mapping properties of the integral operator [I(f)](z) = c/zc-1 ∫z0 ζc/f(ζ)dζ, c > 0. © 2004 by the University of Notre Dame. All rights reserved.