Neighborhoods of certain classes of analytic functions defined using Hadamard product (original) (raw)

Some Properties of a New Class of Analytic Functions Defined In Terms of a Hadamard Product

J. Inequal. Pure Appl. Math, 2008

In this paper we introduce a new class H(φ, α, β) of analytic functions which is defined by means of a Hadamard product (or convolution) of two suitably normalized analytic functions. Several properties like, the coefficient bounds, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are investigated. We further consider a subordination theorem, certain boundedness properties associated with partial sums, an integral transform of a certain class of functions, and some integral means inequalities. Several interesting consequnces of our main results are also pointed out.

On certain p-valently analytic functions involving hadamard products

2008

In this paper, we introduce and study some properties of unified class ( , ; , , ) involving the Hadamard Products given by Juneja et. al in 1985. The properties include coefficient bounds, growth and distortion, and closure theorem. Further, the radii of starlikeness and convexity is also given.

Hadamard product of analytic functions and some special regions and curves

Journal of Inequalities and Applications, 2013

In this paper we present some new applications of convolution and subordination in geometric function theory. The paper deals with several ideas and techniques used in this topic. Besides being an application to those results, it provides interesting corollaries concerning special functions, regions and curves.

On certain applications of the Hadamard product

Applied Mathematics and Computation, 2008

In this paper, we give an extension of the Ö zkan and Altintas ß results [Ö . Ö zkan, O. Altintas ß, Applications of differential subordination, Appl. Math. Lett. 19 (2006) 728-734] on the inclusion relationships involving various subclasses of analytic and univalent functions, defined in terms of linear operators. We show that these classes are closed under convolution with convex functions.

A class of functions defined by using Hadamard Product

Hokkaido Mathematical Journal, 1986

We introduce a class P_{a}[\beta, \gamma] of functions defined by using Hadamard product f*S_{a}(z) of f(z) and S_{a}(z)=z/(1-z)^{2(1-a)}. The object of the present paper is to determine extreme points, coefficient inequalities, distortion theorems, and radii of starlikeness and convexity for functions in P_{a}[\beta, \gamma]. Further, we give distortion theorems for fractional calculus of functions belonging to the class P_{a}[\beta, \gamma] .

Some relations between certain classes of analytic functions

In the present paper we introduce and studied two subclasses of multivalent functions denoted by M λ p,n (γ;β ) and N λ p,n (μ,η;δ ) . Further, by giving specific values of the parameters of our main results, we will find some connection between these two classes, and moreover, several consequences of main results are also discussed.