Univalence criteria for general integral operator
نویسنده
چکیده
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 univalent in the open unit disc U , when fi ∈ Gbi for all i = 1, . . . , n. AMS subject classifications: 30C45
منابع مشابه
Univalence 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 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.
متن کاملUnivalence Criteria for a Nonlinear Integral Operator
The purpose of this paper is to obtain univalence of a certain nonlinear integral transform of functions belonging to a subclass of analytic functions. We also give several interesting geometric properties of the integral transform.
متن کاملOn an integral operator
In this paper we define a general integral operator for analytic functions in the open unit disk and we determine some conditions for univalence of this integral operator.
متن کاملUnivalence preserving integral operators defined by generalized Al-Oboudi differential operators
In this paper, we investigate sufficient conditions for the univalence of an integral operator defined by generalized Al-Oboudi differential operator.
متن کاملA new univalent integral operator defined by Al - Oboudi differential operator 1 Serap Bulut
In [3], Breaz and Breaz gave an univalence condition of the integral operator Gn,α introduced in [2]. The purpose of this paper is to give univalence condition of the generalized integral operator Gn,m,α defined in [4]. Our results generalize the results of [3]. 2000 Mathematics Subject Classification: 30C45.
متن کامل