Univalence, strong starlikeness and integral transforms

M. Obradović; S. Ponnusamy; P. Vasundhra

The search session has expired. Please query the service again.

Displaying similar documents to “Univalence, strong starlikeness and integral transforms”

Strongly gamma-starlike functions of order alpha

Mamoru Nunokawa, Janusz Sokół (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

In this work we consider the class of analytic functions $𝒢 (α, γ)$ , which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Złotkiewicz in Gamma starlike functions, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 28 (1974), 53–58. We discuss the order of strongly starlikeness and the order of strongly convexity in this subclass.

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 $f (z) = \sum_{n = - 1}^{\infty} a ₙ (z - p) ⁿ$ , |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 $α \in [0, 1)$ the authors consider the differential subordination and the differential equation of the Briot-Bouquet type: $p^{1 - α} (z) + \frac{z p^{'} (z)}{δ p^{α} (z) + λ p (z)} ≺ h (z), z \in 𝒰,$ $q^{1 - α} (z) + \frac{n z q^{'} (z)}{δ q^{α} (z) + λ q (z)} = h (z), z \in 𝒰,$ 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 $h$ .

On some simple sufficient conditions for univalence

Nikola Tuneski (2001)

Mathematica Bohemica

Similarity:

In this paper some simple conditions on $f^{'} (z)$ and $f^{''} (z)$ which lead to some subclasses of univalent functions will be considered.

Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions

S. Sivasubramanian, R. Sivakumar, S. Kanas, Seong-A Kim (2015)

Annales Polonici Mathematici

Similarity:

Let σ denote the class of bi-univalent functions f, that is, both f(z) = z + a₂z² + ⋯ and its inverse $f^{- 1}$ are analytic and univalent on the unit disk. We consider the classes of strongly bi-close-to-convex functions of order α and of bi-close-to-convex functions of order β, which turn out to be subclasses of σ. We obtain upper bounds for |a₂| and |a₃| for those classes. Moreover, we verify Brannan and Clunie’s conjecture |a₂| ≤ √2 for some of our classes. In addition, we obtain the Fekete-Szegö...

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 $f (z) = z + \sum_{k = 2}^{\infty} a_{k} z^{k}$ . 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.

On products of starlike functions. I

Georgi Dimkov (1991)

Annales Polonici Mathematici

Similarity:

We deal with functions given by the formula $F (z) = z G^{'} (z) = z \prod_{j = 1}^{n} {(f_{j} (z) / z)}^{a_{j}}$ 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.