Displaying similar documents to “Strongly gamma-starlike functions of order alpha”

Univalence, strong starlikeness and integral transforms

M. Obradović, S. Ponnusamy, P. Vasundhra (2005)

Annales Polonici Mathematici

Similarity:

Let represent the class of all normalized analytic functions f in the unit disc Δ. In the present work, we first obtain a necessary condition for convex functions in Δ. Conditions are established for a certain combination of functions to be starlike or convex in Δ. Also, using the Hadamard product as a tool, we obtain sufficient conditions for functions to be in the class of functions whose real part is positive. Moreover, we derive conditions on f and μ so that the non-linear integral...

On products of starlike functions. I

Georgi Dimkov (1991)

Annales Polonici Mathematici

Similarity:

We deal with functions given by the formula F ( z ) = z G ' ( z ) = z ∏ j = 1 n ( f j ( z ) / z ) a j where f j ( z ) are starlike of order α j and a j are complex constants. In particular, radii of starlikeness and convexity as well as orders of starlikeness and convexity are found.

Sufficient conditions for starlike and convex functions

S. Ponnusamy, P. Vasundhra (2007)

Annales Polonici Mathematici

Similarity:

For n ≥ 1, let denote the class of all analytic functions f in the unit disk Δ of the form f ( z ) = z + ∑ k = 2 ∞ a k z k . For Re α < 2 and γ > 0 given, let (γ,α) denote the class of all functions f ∈ satisfying the condition |f’(z) - α f(z)/z + α - 1| ≤ γ, z ∈ Δ. We find sufficient conditions for functions in (γ,α) to be starlike of order β. A generalization of this result along with some convolution results is also obtained.

Coefficient inequalities for concave and meromorphically starlike univalent functions

B. Bhowmik, S. Ponnusamy (2008)

Annales Polonici Mathematici

Similarity:

Let denote the open unit disk and f: → ℂ̅ be meromorphic and univalent in with a simple pole at p ∈ (0,1) and satisfying the standard normalization f(0) = f’(0)-1 = 0. Also, assume that f has the expansion f ( z ) = ∑ n = - 1 ∞ a ₙ ( z - p ) ⁿ , |z-p| < 1-p, and maps onto a domain whose complement with respect to ℂ̅ is a convex set (starlike set with respect to a point w₀ ∈ ℂ, w₀ ≠ 0 resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by C o ( p ) ( Σ s ( p , w ₀ ) resp.). We prove...

A note on Briot-Bouquet-Bernoulli differential subordination

Stanisława Kanas, Joanna Kowalczyk (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let p , q be analytic functions in the unit disk 𝒰 . For α ∈ [ 0 , 1 ) the authors consider the differential subordination and the differential equation of the Briot-Bouquet type: p 1 - α ( z ) + z p ' ( z ) δ p α ( z ) + λ p ( z ) ≺ h ( z ) , z ∈ 𝒰 , q 1 - α ( z ) + n z q ' ( z ) δ q α ( z ) + λ q ( z ) = h ( z ) , z ∈ 𝒰 , with p ( 0 ) = q ( 0 ) = h ( 0 ) = 1 . The aim of the paper is to find the dominant and the best dominant of the above subordination. In addition, the authors give some particular cases of the main result obtained for appropriate choices of functions h .

Fekete–Szegö Problem for a New Class of Analytic Functions Defined by Using a Generalized Differential Operator

M. K. Aouf, R. M. El-Ashwah, A. A. M. Hassan, A. H. Hassan (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions f ( z ) ∈ 𝒜 for which 1 + 1 b z D α , β , λ , δ n f ( z ) ' D α , β , λ , δ n f ( z ) - 1 ( α , β , λ , δ ≥ 0 ; β > α ; λ > δ ; b ∈ ℂ * ; n ∈ ℕ 0 ; z ∈ U ) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis.

Uniformly starlike functions and uniformly convex functions related to the Pascal distribution

Gangadharan Murugusundaramoorthy, Sibel Yalçın (2021)

Mathematica Bohemica

Similarity:

In this article, we aim to find sufficient conditions for a convolution of analytic univalent functions and the Pascal distribution series to belong to the families of uniformly starlike functions and uniformly convex functions in the open unit disk 𝕌 . We also state corollaries of our main results.

On the class of functions strongly starlike of order α with respect to a point

Adam Lecko (1998)

Annales Polonici Mathematici

Similarity:

We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).