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Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator

M. Aouf, A. Shamandy, A. Mostafa, S. Madian (2010)

Annales UMCS, Mathematica

Let A denote the class of analytic functions with the normalization f(0) = f'(0) - 1 = 0 in the open unit disc U = {z : |z| < 1}. Set [...] and define ∞nλ, μ in terms of the Hadamard product [...] . In this paper, we introduce several subclasses of analytic functions defined by means of the operator Inλ, μ A → A, given by [...] . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Inclusion relationships between classes of functions defined by subordination

Jacek Dziok (2011)

Annales Polonici Mathematici

The purpose of the present paper is to investigate various inclusion relationships between several classes of analytic functions defined by subordination. Many interesting applications involving the well-known classes of functions defined by linear operators are also considered.

Indépendance linéaire et algébrique de fonctions liées à la fonction q -dzeta

Jean-Paul Bézivin (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

Pour q ∈ ℂ , | q | &lt; 1 , on définit la q -analogue de la fonction zeta de Riemann par les égalités ζ q ( k ) = ∑ n ≥ 1 σ k - 1 ( n ) q n = ∑ n ≥ 1 n k - 1 q n 1 - q n .Dans [8], W. Zudilin énonce deux questions à propos de ces fonctions de q . La première concerne l’indépendance linéaire sur ℂ ( q ) des fonctions ζ q ( k ) , pour k ≥ 1 , et la seconde l’indépendance algébrique sur ℂ ( q ) des fonctions ζ q ( 2 ) , ζ q ( 4 ) , ζ q ( 6 ) , et des fonctions ζ q ( 2 k + 1 ) , k ≥ 0 . Dans [5], Y. Pupyrev répond positivement à la première question, et donne des résultats partiels pour la seconde.Dans cet article, nous considérons la fonction L ( x , y ) = ∑ n ≥ 1 y n x n 1 - x n , et, avec τ = y d d y , les...

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

Paneva-Konovska, Jordanka (2012)

Mathematica Balkanica New Series

MSC 2010: 33E12, 30A10, 30D15, 30E15We consider some families of 3-index generalizations of the classical Mittag-Le²er functions and study the behaviour of these functions in domains of the complex plane. First, some inequalities in the complex plane and on its compact subsets are obtained. We also prove an asymptotic formula for the case of "large" values of the indices of these functions. Similar results have also been obtained by the author for the classical Bessel functions and their Wright's...

Inequalities concerning polar derivative of polynomials

Arty Ahuja, K. Dewan, Sunil Hans (2011)

Annales UMCS, Mathematica

In this paper we obtain certain results for the polar derivative of a polynomial [...] , having all its zeros on [...] which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.

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