Displaying similar documents to “Uniformly starlike functions and uniformly convex functions related to the Pascal distribution”

Sufficient conditions for starlike and convex functions

S. Ponnusamy, P. Vasundhra (2007)

Annales Polonici Mathematici

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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.

Univalence, strong starlikeness and integral transforms

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

Annales Polonici Mathematici

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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...

Strongly gamma-starlike functions of order alpha

Mamoru Nunokawa, Janusz Sokół (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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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

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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...

Coefficient bounds for some subclasses of p-valently starlike functions

C. Selvaraj, O. S. Babu, G. Murugusundaramoorthy (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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For functions of the form f ( z ) = z p + ∑ n = 1 ∞ a p + n z p + n we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.

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

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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...

On products of starlike functions. I

Georgi Dimkov (1991)

Annales Polonici Mathematici

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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.

On a subclass of α -uniform convex functions

Mugur Acu (2005)

Archivum Mathematicum

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In this paper we define a subclass of α -uniform convex functions by using the S’al’agean differential operator and we obtain some properties of this class.

A note on Briot-Bouquet-Bernoulli differential subordination

Stanisława Kanas, Joanna Kowalczyk (2005)

Commentationes Mathematicae Universitatis Carolinae

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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 .