On the Radii of univalence of Gel'fond-Leont'ev derivatives
Abstract
Let 0<R<+∞, let A(R) bethe class of functions f(z)=∞∑k=0fkzk, analytic in {z:|z|<R}, and let l(z)=∞∑k=0lkzk,lk>0 be a formal power series. We prove that if l2k/lk+1lk−1 is a nonincreasing sequence, f∈A(R), and |fk/fk+1↗R,k→∞,0<R<+∞, then the sequence (ρn) of radii of univalence of the Gel'fondLeont'ev derivatives satisfies the relation Dnlf(z)=∞∑k=0lkfk+nlk+nzk The case where the condition |fk/fk+1|↗R,k→∞, is not satisfied is also considered.
Published
25.03.1995
How to Cite
Sheremeta, M. M. “On the Radii of Univalence of Gel’fond-Leont’ev Derivatives”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 47, no. 3, Mar. 1995, pp. 390–399, https://umj.imath.kiev.ua/index.php/umj/article/view/5428.
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Section
Research articles