scholarly journals Coefficients assessment for certain subclasses of bi-univalent functions related with quasi-subordination

2020 ◽  
Vol 108 (122) ◽  
pp. 155-162
Author(s):  
Sibel Yalçın ◽  
Waggas Atshan ◽  
Haneen Hassan
Keyword(s):  
Univalent Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disc

We investigate specific new subclasses of the function class ? of bi-univalent function defined in the open unit disc, which is connected with quasi-subordination. We find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these subclasses. Already pointed out are some documented and new implications of those findings.

scholarly journals Coefficient Bounds for Certain Subclasses of Bi-Univalent Function

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh ◽  
V. Prameela
Keyword(s):  
Univalent Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Bounds

We introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients|a2|and|a3|for functions in these new subclasses. Also consequences of the results are pointed out.

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 Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 418 ◽  
Author(s):  
Sheza M. El-Deeb ◽  
Teodor Bulboacă ◽  
Bassant M. El-Matary
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients a 2 and a 3 for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class.

scholarly journals Maclaurin Coefficient Estimates for New Subclasses of Bi-univalent Functions Connected with a q-Analogue of Bessel Function

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Sheza M. El-Deeb
Keyword(s):  
Bessel Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce new subclasses of the function class Σ of bi-univalent functions connected with a q-analogue of Bessel function and defined in the open unit disc. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients a2 and a3 for functions in these new subclasses.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

scholarly journals On Some Subclasses of $m$-fold Symmetric Bi-univalent Functions associated with the Sakaguchi Type Functions

2021 ◽  
pp. 1-15
Author(s):  
Ismaila O. Ibrahim ◽  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

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.

Majorization-Subordination Theorems for Locally Univalent Functions, II

1973 ◽  
Vol 25 (2) ◽  
pp. 420-425 ◽  
Author(s):  
Douglas Michael Campbell
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Family ◽  
Linear Invariant ◽  
Linear Invariant Family

Let denote the set of all normalized analytic univalent functions in the open unit disc D. Let f(z), F(z) and φ(z) be analytic in |z| < r. We say that f(z) is majorized by F(z) in we say that f(z) is subordinate to F(z) in where .Let be the set of all locally univalent (f’(z) ≠ 0) analytic functions in D with order ≦α which are of the form f(z) = z +… . The family is known as the universal linear invariant family of order α [6]. A concise summary of and introduction to properties of linear invariant families which relate to the following material is contained in [1]. The present paper contains the proofs of some of the results announced in [1]

scholarly journals New Subclasses concerning Some Analytic and Univalent Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Maslina Darus ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Analytic And Univalent Functions

Considering a function f(z)=z/1-z2 which is analytic and starlike in the open unit disc U and a function f(z)=z/1-z which is analytic and convex in U, we introduce two new classes Sα⁎(β) and Kα(β) concerning fα(z)=z/1-zα  (α>0). The object of the present paper is to discuss some interesting properties for functions in the classes Sα⁎(β) and Kα(β).

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