Starlikeness Conditions for an Integral Operator
نویسندگان
چکیده
Let for fixed n ∈ N, Σn denotes the class of function of the following form f(z) = 1 z + ∞ ∑ k=n akz , which are analytic in the punctured open unit disk ∆∗ = {z ∈ C : 0 < |z| < 1}. In the present paper we defined and studied an operator in F (z) = [ c+ 1− μ zc+1 ∫ z 0 ( f(t) t )μ tdt ] 1 μ , for f ∈ Σn and c+ 1− μ > 0.
منابع مشابه
Starlikeness Properties of a New Integral Operator for Meromorphic Functions
Aabed Mohammed and Maslina Darus School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D. Ehsan, Malaysia Correspondence should be addressed to Maslina Darus, [email protected] Received 3 March 2011; Revised 15 April 2011; Accepted 3 June 2011 Academic Editor: Pablo Gonza’lez-Vera Copyright q 2011 A. Mohammed and M. Darus. This is...
متن کاملOzaki's conditions for general integral operator
Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*} mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*} ma...
متن کاملOn a Certain Subclass of Analytic Functions Involving the Al-oboudi Differential Operator
Abstract: In this paper we introduce a new subclass of normalized analytic functions in the open unit disc which is defined by the Al-Oboudi differential operator. A coefficient inequality, extreme points and integral mean inequalities of a differential operator for this class are given. We investigate various subordination results for the subclass of analytic functions and obtain sufficient co...
متن کاملOn a Certain Class of Meromorphic Functions Associated with a Differential Operator
In this paper, we introduce and investigate a new class of meromorphic functions defined by a differential operator. For this class, we obtain coefficient inequality, distortion inequality, radius of close-to-convex, starlikeness and convexity, extreme points and integral means inequality.
متن کاملOn Applications of Generalized Integral Operator to a Subclass of Analytic Functions
Making use of generalized integral operator, we define a subclass of analytic functions with negative coefficients. The main object of this paper is to obtain coefficient estimates, closure theorems and extreme points. Also we obtain radii of close-to-convexity, starlikeness and convexity and neighbourhood results for functions in the generalized classR∗(α, β, μ, η). 2000 Mathematics Subject Cl...
متن کامل