Some Properties of a Subclass of Uniformly Convex Functions With Negative Coefficients

Abstract

Abstract. 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 TS\ (n,a,β) of uniformly convex functions with negative coefficients. We also derive many results for the modified Hadamard products of functions belonging to the class TS\ (n,a, β), 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.

New Subclasses of Multivalent Analytic Functions Associated with a Linear Operator

“…In the present paper, we prove a number of theorems involving the modified Hadamard products, integral transforms, and the partial sums of functions in the classes , ( , , , , ) and , ( , , , , ). Some of our results are generalizations of the corresponding results in [4][5][6][7][8][9].…”

“…with = 1 was studied by Aouf [8] and Aouf et al [6]. Recently, Aouf [9] investigated the modified Hadamard products of several functions in the classes ( , , ) and ( , , ) for ∈ .…”

Properties of Certain Class of Uniformly Starlike and Convex Functions Defined by Convolution

“…?, ? ?, respectively, we obtain the results obtained by Aouf and Mostafa [3,Theorem 11,and Corollaries 5,6,respectively].…”

Characterizations for New Classes of Analytic Functions Defined By Using Salagean Operator

“…Let A denote the class of functions of the form   (see Eker and Owa [4]) Rosy and Mumgundaramorthy [5], Asurf [6])…”