منابع مشابه
Univalence Criteria for a General Integral Operator
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متن کاملUnivalence 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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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: Abstract and Applied Analysis
سال: 2011
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2011/759175