Study of some subclasses of univalent functions and their radius properties

An analytic function f(z) = z + a2z2 + ⃛ in the unit disk Δ = {z : |z| < 1} is said to be in if for some λ ≥ 0 and μ > -1. For -1 ≤ α ≤ 1, we introduce a geometrically motivated -class defined by where represents the class of all normalized univalent functions in Δ. In this paper, the authors determine necessary and sufficient coefficient conditions for certain class of functions to be in. Also, radius properties are considered for -class in the class. In addition, we also find disks |z| <r:=r(λ;μ) for which whenever. In addition to a number of new results, we also present several new sufficient conditions for f to be in the class. © 2006, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.