On the Radii of univalence of Gel’fond-Leont’ev derivatives
Let 0 < R < +∞, let A(R) bethe class of functions f(z) = _k=0^∞f_kz^k, analytic in { z: |z| < R }, and let l(z) = _k=0^∞l_kz^k, l_k > 0 be a formal power series. We prove that if l^2_k/l_k+1l_k-1 is a nonincreasing sequence, f A(R), and |f_k/f_k+1 earrow R, k → ∞, 0 < R < +∞, then the sequence (ρ_n) of radii of univalence of the Gel’fondLeont’ev derivatives satisfies the relation D^n_lf(z) = _k=0^∞l_kf_k+n l_k+n z_k The case where the condition |f_k/f_k+1| earrow R,k → ∞, is not satisfied is also considered., number=3, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Sheremeta, M. M., year=1995, month=Mar., pages=390–399