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Some properties of a subclass of uniformly convex functions with negative coefficients

Aouf M., Mostafa A.

Demonstratio Mathematica

2008

Vol. 41, nr 2

353-370

The aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass TSlambda (n,alpha, beta) of uniformly convex functions with negative coefficients. We also derive many results for the modified Hadamard products of functions belonging to the class TSlambda(n,alpha, beta), and obtain several interesting distortion theorems for certain fractional operators of functions in this class. Finally, we consider integral operators associated with functions in this class.

On partial sums of certain analytic functions

Mostafa A.

Demonstratio Mathematica

2008

Vol. 41, nr 4

779-789

In the present paper we give some results concerning partial sums of certain analytic functions analogous to the results due to H. Silverman [J. Math. Anal. Appl. 209 (1997), 221-227]. All the results are sharp.

Generalizations of Hadamard products of certain meromorphic univalent functions with positive coefficients

Aouf M., Silverman H.

Demonstratio Mathematica

2008

Vol. 41, nr 2

381-388

The authors establish certain results concerning the generalized Hadamard products of certain meromorphic univalent functions with positive coefficients analagous to the results due to Choi et al. (J. Math. Anal. Appl. 199(1996), 495-501).

Distortion theorems in the class Kn(D)

Kir'yatskii E. G.

Demonstratio Mathematica

2008

Vol. 41, nr 3

543-549

This article presents the analysis of properties of functions belonging to the class Kn(D) earlier introduced by the author. This is a class of functions analytical in the domain D, for which the n-th divided difference [F; zo, . . . , zn] [...]consisting of functions univalent in the domain D is obtained. The subclass Kn(E), formed by functions F(z) = zn + an+izn+1 + .... analytical in a unit circle E is separated from class Kn(D) and its properties are considered. The author touches classical and at the same time urgent questions, arising at the study of analytical functions, belonging to some class.