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3 Demonstratio Mathematica

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

100%

Aouf M. , Mostafa A.

tom 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.

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

100%

Aouf M. , Silverman H.

tom 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).

Fixed coefficients for certain subclasses of starlike functions with negative coefficients

100%

Aouf M. , Al-Dohiman A.

tom Vol. 38, nr 3

551--565

The main object of this paper is to study the class T*n,c(alfa,beta) of analytic functions with negative coefficients and with fixed second coefficients. Among other results of interest, we derive coefficient estimates, closure properties involving convex linear combinations, growth and distortion theorems, and radii of starlikeness and convexity for functions in the class T*n,c(alfa,beta). Many of these results are further extended to hold true for families of functions with finitely many fixed coefficients.