On Generalized Bazilevic Functions Related with Conic Regions (original) (raw)

On Certain Generalized Bazilevic Type Functions Associated with Conic Regions

Let f and g be analytic in the open unit disc and, for α, β ≥ 0, let The main aim of this paper is to study the class of analytic functions which map J (α, β, f, g) onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.

On a Class of Family of Bazilevic Functions

2010

In this paper the author introduce and study a more generalized class of the family of Bazilevic functions by using derivative operator under which we consider coefficient inequalities, inclusion relation, extremal problem, and coefficient bounds. The consequences of parametrics are also discussed.

On a new class of analytic functions associated with conic domain

Computers & Mathematics with Applications, 2011

The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk E onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain.

Some remarks on certain Bazilevic functions

Journal of the Nigerian Association of Mathematical Physics, 2008

In this note we give some sufficient conditions for an analytic function f (z) normalized by f (0) = 1 to belong to certain subfamilies of the class of Bazilevic functions. In earlier works, the closure property of many classes of functions under the Bernardi integral have been considered. The converse of this problem is also considered here.

Some Properties of Analytic Functions Associated with Conic Type Regions

2018

The main purpose of this investigation is to define new subclasses of analytic functions with respect to symmetrical points. These functions map the open unit disk onto certain conic regions in the right half plane. We consider various corollaries and consequences of our main results. We also point out relevant connections to some of the earlier known developments.

Generalized Class of Sakaguchi Functions in Conic Region

In this paper, we use the concept of Sakaguchi type functions, Janowski functions and the conic regions are combined to define a class of functions in a new interesting conic domain. We prove coefficient inequalities and inclusion results.

Properties of Spiral-Like Close-to-Convex Functions Associated with Conic Domains

Mathematics, 2019

In this paper, our aim is to define certain new classes of multivalently spiral-like, starlike, convex and the varied Mocanu-type functions, which are associated with conic domains. We investigate such interesting properties of each of these function classes, such as (for example) sufficiency criteria, inclusion results and integral-preserving properties.

On Janowski Close-to-Convex Functions Associated with Conic Regions

International Journal of Analysis and Applications

In this work, we introduce and investigate a class of analytic functions which is a subclass of close-to-convex functions of Janowski type and related to conic regions. Length of the image curve |z| = r < 1 under the generalized Janowski close-to-convex function is derived. Furthermore, rate of growth of coefficients and Hankel determinant for this class are obtained. Relevant connections of our results with the earlier known results are also pointed out.

Applications of certain operators to the classes of analytic functions related with generalized conic domains

Computers & Mathematics with Applications, 2011

Let A be the class of functions f : f (z) = z + ∑ ∞ n=2 a n z n , which are analytic in the open unit disc E. We use a linear operator closely related to the multiplier transformation to introduce and investigate certain subclasses of A which map E onto a generalized form of the conic domain. Several properties of these classes including some inclusion relations, convolution and other class preserving operators are studied. In particular, we derive many known and new results as special cases. Applications of some results are also given.