scholarly journals Based on a family of bi-univalent functions introduced through the Faber polynomial expansions and Noor integral operator

2022 ◽  
Vol 7 (4) ◽  
pp. 5146-5155
Author(s):  
F. Müge Sakar ◽  
◽  
Arzu Akgül ◽  
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Polynomial Expansions

<abstract><p>In this study, by using $ q $-analogue of Noor integral operator, we present an analytic and bi-univalent functions family in $ \mathfrak{D} $. We also derive upper coefficient bounds and some important inequalities for the functions in this family by using the Faber polynomial expansions. Furthermore, some relevant corollaries are also presented.</p></abstract>

scholarly journals A Subclass of Bi-Univalent Functions Based on the Faber Polynomial Expansions and the Fibonacci Numbers

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 160
Author(s):  
Şahsene Altınkaya ◽  
Sibel Yalçın ◽  
Serkan Çakmak
Keyword(s):  
Integral Operator ◽  
Univalent Function ◽  
Fibonacci Numbers ◽  
Univalent Functions ◽  
Function Class ◽  
Faber Polynomial ◽  
New Class ◽  
Polynomial Expansions

In this investigation, by using the Komatu integral operator, we introduce the new class of bi-univalent functions based on the rule of subordination. Moreover, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general coefficient of the bi-univalent function class.

Faber polynomial coefficient estimates for a certain subclass of meromorphic bi-univalent functions

2019 ◽  
Vol 13 (04) ◽  
pp. 2050076 ◽  
Author(s):  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Univalent Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Polynomial Expansions

In this paper, by using the Faber polynomial expansions we can find the coefficient bounds for [Formula: see text] subclass of meromorphic bi-univalent functions. The results presented in this paper would generalize and improve some recent works.

scholarly journals Faber polynomial coefficient estimates for a subclass of analytic bi-univalent functions

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1567-1575 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Univalent Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Polynomial Expansions

In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor-Maclaurin coecients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

scholarly journals Coefficient bounds for a certain class of analytic and bi-univalent functions

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1839-1845 ◽  
Author(s):  
H.M. Srivastava ◽  
Sevtap Eker ◽  
Rosihan Alic
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
Recent Developments ◽  
Polynomial Expansions

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk U. By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1(Suppl.)) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

scholarly journals Coefficient problems for certain subclass of m-fold symmetric bi-univalent functions by using Faber polynomial

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2573-2583
Author(s):  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomial ◽  
Coefficient Problems ◽  
Polynomial Expansions

In this paper, we apply the Faber polynomial expansions to find upper bounds for the general coefficients |amk+1| (k >= 3) of functions in the subclass N?m (?,?;?). The results presented in this paper would generalize and improve some recent works.

scholarly journals Coefficients Estimates of the Class of Biunivalent Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-4
Author(s):  
Abdullah Aljouiee ◽  
Pranay Goswami
Keyword(s):  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Polynomial Expansions

Applying the Faber polynomial expansions, we obtain the general coefficient bounds for the class of biunivalent functions with bounded boundary rotations.

scholarly journals Coefficients of Meromorphic Bi-Bazilevic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Jay M. Jahangiri ◽  
Samaneh G. Hamidi
Keyword(s):  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Polynomial Expansions ◽  
Bazilevic Functions

A function is said to be bi-Bazilevic in a given domain if both the function and its inverse map are Bazilevic there. Applying the Faber polynomial expansions to the meromorphic Bazilevic functions, we obtain the general coefficient bounds for bi-Bazilevic functions. We also demonstrate the unpredictability of the behavior of early coefficients of bi-Bazilevic functions.

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