Univalence Conditions Related to a General Integral Operator
نویسندگان
چکیده
منابع مشابه
Univalence conditions for a general integral operator
For analytic functions in the open unit disk U , we define a new general integral operator. The main object of the this paper is to study this new integral operator and to determine univalence conditions of it. Several corollaries of the main results are also considered.
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For analytic functions in the open unit disk, J. Becker (Math. Ann. 202(1973)) has given some univalent conditions. In the present paper, some extensions of Becker’s type are considered.
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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.
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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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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2012
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2012/140924