Radius of Limaçon starlikeness for Janowski starlike functions

2021 ◽  
Author(s):  
R. Kanaga ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disc ◽  
Starlike Functions ◽  
Starlike Function ◽  
Open Unit ◽  
Open Unit Disc ◽  
Class Of Functions

Let [Formula: see text] be an analytic function defined on the open unit disc [Formula: see text], with [Formula: see text], satisfying the subordination [Formula: see text], where [Formula: see text]. The domain [Formula: see text] is bounded by a Limaçon and the function [Formula: see text] is called starlike function associated with Limaçon domain. For [Formula: see text], we find the smallest disc [Formula: see text] and the largest disc [Formula: see text], centered at [Formula: see text] such that the domain [Formula: see text] is contained in [Formula: see text] and contains [Formula: see text]. By using this result, we find the radius of Limaçon starlikeness for the class of starlike functions of order [Formula: see text] [Formula: see text] and the class of functions [Formula: see text] satisfying [Formula: see text], [Formula: see text]. We give extension of our results for Janowski starlike functions.

scholarly journals Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 783 ◽  
Author(s):  
Ibtisam Aldawish ◽  
Tariq Al-Hawary ◽  
B. A. Frasin
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Open Unit Disc ◽  
Class A ◽  
Class Of Functions

Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

scholarly journals A CONVOLUTION APPROACH TO CERTAIN SUBCLASSES OF STARLIKE FUNCTIONS

1992 ◽  
Vol 23 (4) ◽  
pp. 311-320
Author(s):  
T . RAM REDDY ◽  
O. P. JUNEJA ◽  
K. SATHYANARAYANA
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Integral Transforms ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disc ◽  
Containment Property ◽  
Convolution Approach

The class $R_\gamma(A,B)$ for $-1\le B < A\le 1$ and $\gamma> (A- 1)/(1- B)$ consisting of normalised analytic functions in the open unit disc is defined with the help of Convolution technique. It consists of univalent starlike functions for $\gamma\ge 0$. We establish containment property, integral transforms and a sufficient condition for an analytic function to be in $R\gamma(A,B)$. Using the concept of dual spaces we find a convolution condition for a function in this class.

scholarly journals The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Unit Disc ◽  
Harmonic Mapping ◽  
Starlike Functions ◽  
Starlike Function ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form defined on the open unit disc . The functions are in the class of the generalized Janowski starlike log-harmonic mapping, , with the functional in the class of the generalized Janowski starlike functions, . By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, .

scholarly journals Second Hankel Determinants for Some Subclasses of Biunivalent Functions Associated with Pseudo-Starlike Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
K. Rajya Laxmi ◽  
R. Bharavi Sharma
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Starlike Function ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Hankel Determinants ◽  
Second Hankel Determinant ◽  
Starlike Univalent Function

We introduce second Hankel determinant of biunivalent analytic functions associated with λ-pseudo-starlike function in the open unit disc Δ subordinate to a starlike univalent function whose range is symmetric with respect to the real axis.

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

scholarly journals Hankel determinant for certain class of analytic function defined by generalized derivative operator

2012 ◽  
Vol 43 (3) ◽  
pp. 445-453
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Upper Bound ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Generalised Derivatives

The authors in \cite{mam1} have recently introduced a new generalised derivatives operator $ \mu_{\lambda _1 ,\lambda _2 }^{n,m},$ which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator $\mu_{\lambda_1 ,\lambda _2 }^{n,m}$, the authors derive the class of function denoted by $ \mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$, which contain normalised analytic univalent functions $f$ defined on the open unit disc $U=\left\{{z\,\in\mathbb{C}:\,\left| z \right|\,<\,1} \right\}$ and satisfy \begin{equation*}{\mathop{\rm Re}\nolimits} \left( {\mu _{\lambda _1 ,\lambda _2 }^{n,m} f(z)} \right)^\prime > 0,\,\,\,\,\,\,\,\,\,(z \in U).\end{equation*}This paper focuses on attaining sharp upper bound for the functional $\left| {a_2 a_4 - a_3^2 } \right|$ for functions $f(z)=z+ \sum\limits_{k = 2}^\infty {a_k \,z^k }$ belonging to the class $\mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$.

scholarly journals Functions starlike with respect to other points

1991 ◽  
Vol 14 (3) ◽  
pp. 451-456 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Real ◽  
Symmetric Points ◽  
Class Of Functions

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. Forp≤β<1, letSS*(β)be the class of normalised analytic functionsfdefined in the open unit discDsuch thatRezf′(z)/(f(z)−f(−z))>β, for somez ϵ D. In this paper, we introduce 2 other similar classesSC*(β),SSC*(β)as well as give sharp results for the real part of some function forf ϵ SS*(β),SC*(β)andSSC*(β)The behaviour of certain integral operators are also considered.

scholarly journals Some uniformly starlike functions with varying arguments

2004 ◽  
Vol 35 (1) ◽  
pp. 23-28 ◽  
Author(s):  
K. Vijaya ◽  
G. Murugusundaramoorthy
Keyword(s):  
Unit Disc ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Bound ◽  
Uniformly Starlike Functions ◽  
Uniformly Starlike ◽  
Varying Arguments

In this paper two new subclasses of starlike functions that are analytic and normalized in the open unit disc with varying arguments is introduced. For functions in these classes we obtained coefficient bound, distortion results and the extreme points.

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