منابع مشابه
Univalence criteria for general integral operator
Let A be the class of all analytic functions which are analytic in the open unit disc U = {z : |z| < 1} and Gb = { f ∈ A : ∣∣∣∣ 1 + zf ′′(z)/f ′(z) zf ′(z)/f(z) − 1 ∣∣∣∣ < b, z ∈ U } . In this paper, we derive sufficient conditions for the integral operator Ii γ (f1, ..., fn)(z) = z ∫ 0 tγ−1 ( f ′ 1(t) )α1 ( f1(t) t )1−α1 ... ( f ′ n(t) )αn ( fn(t) t )1−αn dt 1 γ to be analytic and ...
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This note is a sequel to our paper [OS] where we generalized the Schwarzian derivative to conformal mappings of Riemannian manifolds. There we found that many of the phenomena familiar from the classical theory have counterparts in the more general setting. Here we advance this another step by giving a generalization of the well known univalence criterion of Nehari [N]. Despite its relatively a...
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In this work we consider some integral operators for analytic functions in the open unit disk and we obtain new univalence criteria for these integral operators, using Mocanu’s and Şerb’s Lemma, Pascu’s Lemma. Mathematics Subject Classification (2010): 30C45.
متن کاملUnivalence Criteria for a General Integral Operator
In this paper the author introduces a general integral operator and determines conditions for the univalence of this integral operator. Also, the significant relationships and relevance with other results are also given.
متن کاملUnivalence Criteria in Multiply-connected Domains
Theorems due to Nehari and Ahlfors give sufficient conditions for the univalence of an analytic function in relation to the growth of its Schwarzian derivative. Nehari's theorem is for the unit disc and was generalized by Ahifors to any simply-connected domain bounded by a quasiconformal circle. In both cases the growth is measured in terms of the hyperbolic metric of the domain. In this paper ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1983
ISSN: 0019-2082
DOI: 10.1215/ijm/1256046499