scholarly journals Initial Coefficients of Biunivalent Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
See Keong Lee ◽  
V. Ravichandran ◽  
Shamani Supramaniam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases

An analytic functionfdefined on the open unit disk is biunivalent if the functionfand its inversef-1are univalent in𝔻. Estimates for the initial coefficients of biunivalent functionsfare investigated whenfandf-1, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
S. P. Goyal ◽  
Rakesh Kumar
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

AbstractIn the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f

scholarly journals Coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions

2021 ◽  
Vol 66 (4) ◽  
pp. 659-666
Author(s):  
Abbas Kareem Wanas ◽  
◽  
Agnes Orsolya Pall-Szabo ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Special Cases

In the present paper, we introduce and study two new subclasses of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients $\left| a_{m+1}\right|$ and $\left| a_{2m+1}\right|$. Also, we indicate certain special cases for our results.

scholarly journals Initial coefficient estimates for a classes of m-fold symmetric bi-univalent functions involving Mittag-Leffler function

2020 ◽  
Vol 24 (2) ◽  
pp. 51-61
Author(s):  
Abbas Wanas ◽  
Huo Tang
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Initial Coefficient ◽  
Special Cases

The main object of the present paper is to use Mittag-Leffler function to introduce and study two new classes RSm(g, l, e, d, t ; a) and R * Sm(g, l, e, d, t ; b) of Sm consisting of analytic and m-fold symmetric bi-univalent functions defined in the open unit disk U. Also, we determine the estimates on the initial coefficients |am+1| and |a2m+1| for functions in each of these new classes. Furthermore, we indicate certain special cases for our results.

scholarly journals Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator

2021 ◽  
Vol 5 (1) ◽  
pp. 42-50
Author(s):  
Timilehin Gideon Shaba ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Special Cases

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.

scholarly journals Coefficients Bounds for a General Subclasses of m-Fold Symmetric Bi-Univalent Functions

2017 ◽  
Vol 9 (2) ◽  
pp. 33-39 ◽  
Author(s):  
Waggas Galib Atshan ◽  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases

 In this paper, we introduce and investigate a new general subclasses and  of  consisting of analytic and m-fold symmetric  bi-univalent functions in the open unit disk  We obtain estimates on the Taylor-Maclaurin coefficients  and  Also, we obtain new special cases for our results.

scholarly journals Coefficient estimates for some subclasses of bi-univalent functions related to m-fold symmetry

2019 ◽  
Vol 11 (2) ◽  
pp. 81-86
Author(s):  
Waggas Galib Atshan ◽  
Salwa Kalf Kazim
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Special Cases

The purpose of present paper is to introduce and  investigate two new subclasses    and  of analytic and m-fold symmetric bi- univalent functions in the  open unit disk . Among other results belonging to these subclasses upper coefficients bounds   and  are obtained in this study. Certain special cases are also indicated .  

scholarly journals Fekete-Szegö Problems for Quasi-Subordination Classes

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk

An analytic functionfis quasi-subordinate to an analytic functiong, in the open unit disk if there exist analytic functionsφandw, with|φ(z)|≤1,w(0)=0and|w(z)|<1such thatf(z)=φ(z)g(w(z)). Certain subclasses of analytic univalent functions associated with quasi-subordination are defined and the bounds for the Fekete-Szegö coefficient functional|a3-μa22|for functions belonging to these subclasses are derived.

scholarly journals On a Length Problem for Univalent Functions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 266 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół ◽  
Nak Cho
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk

Let g be an analytic function with the normalization in the open unit disk. Let L ( r ) be the length of g ( { z : | z | = r } ) . In this paper we present a correspondence between g and L ( r ) for the case when g is not necessary univalent. Furthermore, some other results related to the length of analytic functions are also discussed.

scholarly journals Subordination by convex functions

2006 ◽  
Vol 2006 ◽  
pp. 1-6 ◽  
Author(s):  
Rosihan M. Ali ◽  
V. Ravichandran ◽  
N. Seenivasagan
Keyword(s):  
Analytic Function ◽  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Subordination Result ◽  
Special Cases

For a fixed analytic functiong(z)=z+∑n=2∞gnzndefined on the open unit disk andγ<1, letTg(γ)denote the class of all analytic functionsf(z)=z+∑n=2∞anznsatisfying∑n=2∞|angn|≤1−γ. For functions inTg(γ), a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.

scholarly journals Coefficient Bounds and Fekete-Szegӧ Problem for a New Subclasses of Holomorphic Bi-Univalent Functions Defined by Horadam polynomials

2021 ◽  
Vol 26 (2) ◽  
pp. 52-65
Author(s):  
Najah Ali Jiben Al-Ziadi ◽  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Special Cases

In the present paper, by making use the Horadam polynomials, we introduce and investigate two new subclasses  and  of the function class  of holomorphic bi-univalent functions in the open unit disk Δ. For functions belonging to this subclasses, we obtain upper bounds for the second and third coefficients and discuss Fekete-Szegӧ problem. Furthermore, we point out several new special cases of our results.

Sign in / Sign up

Export Citation Format

Share Document