Displaying similar documents to “A class of analytic functions defined by Ruscheweyh derivative”

Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

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Let p ' and q ' be points in ℝ n . Write p ' ∼ q ' if p ' - q ' is a multiple of ( 1 , ... , 1 ) . Two different points p and q in ℝ n / ∼ uniquely determine a tropical line L ( p , q ) passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on n leaves. It is also a metric graph. If some representatives p ' and q ' of p and q are the first and second columns of some real normal idempotent order n matrix A , we prove that the tree L ( p , q ) is described by a matrix F , easily obtained from A . We also...

On certain subclasses of bounded univalent functions

J. Fuka, Z. J. Jakubowski (1991)

Annales Polonici Mathematici

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Let = z ∈ ℂ; |z| < 1, T = z ∈ ℂ; |z|=1. Denote by S the class of functions f of the form f(z) = z + a₂z² + ... holomorphic and univalent in , and by S(M), M > 1, the subclass of functions f of the family S such that |f(z)| < M in . We introduce (and investigate the basic properties of) the class S(M,m;α), 0 < m ≤ M < ∞, 0 ≤ α ≤ 1, of bounded functions f of the family S for which there exists an open a r c I α = I α ( f ) ⊂ T of length 2πα such that l i m ¯ z → z ₀ , z ∈ | f ( z ) | ≤ M for every z ₀ ∈ I α and l i m ¯ z → z ₀ , z ∈ | f ( z ) | ≤ m for every z ₀ ∈ T Ī α .

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n ∂ ∂ x n on ℝ n is proved. In this note there is shown that in the cases k ≠ 0 , k ≠ 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.

Fekete-Szegö Inequality for Universally Prestarlike Functions

Shanmugam, T., Lourthu Mary, J. (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 30C45 The universally prestarlike functions of order α ≤ 1 in the slit domain Λ = C [1;∞) have been recently introduced by S. Ruscheweyh. This notion generalizes the corresponding one for functions in the unit disk Δ (and other circular domains in C). In this paper, we obtain the coefficient inequalities and the Fekete-Szegö inequality for such functions.