doiSerbia

Radius of univalence of certain class of analytic functions

Obradović M. (Department of Mathematics, Faculty of Civil Engineering, University of Belgrade, Belgrade)
Ponnusamy S. (Department of Mathematics, Indian Institute of Technology Madras, Chennai, India)

Let A denote be the class of analytic functions in the unit disk D with the normalization ƒ(0) = ƒ'(0) - 1 = 0. For z/ƒ (z) ≠ 0 in D, consider Uƒ (z) = z/f(z)2ƒ'(z) and B(z) = f(z)/z. Under a suitable condition on Ω we determine the radius of univalence of ƒ whenever Uƒ (z) є Ω or B(z) є Ω for z є D.

Keywords: Coefficient inequality, analytic, univalent, and Bazilevič functions, radius of univalence