scholarly journals Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

2021 ◽  
Vol 25 (1) ◽  
pp. 71-80
Author(s):  
Serap Bulut ◽  
Wanas Kareem
Keyword(s):  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Special Cases

The main purpose of this manuscript is to find upper bounds for the second and third Taylor-Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Ruscheweyh derivative operator. Further, we point out certain special cases for our results.

scholarly journals Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 172 ◽  
Author(s):  
Hari M. Srivastava ◽  
Ahmad Motamednezhad ◽  
Ebrahim Analouei Adegani
Keyword(s):  
Fractional Derivative ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Faber Polynomial

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published 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 Some Results of Differential Subordination and Differential Superordination Theorems for Univalent Functions Defined by Ruscheweyh Derivative Operator

2019 ◽  
Vol 3 (2) ◽  
pp. 432
Author(s):  
Aqeel AL-khafaji
Keyword(s):  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Creative Commons ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Differential Superordination ◽  
Open Access Article

The purpose of the present paper is to derive several subordination, superordination results, and sandwich results for the function of the form $f\left(z\right)=z+\sum^{\infty }_{n=2}{a_nz^n}$ which is univalent in the open unit disc $\ U=\left\{z\in \mathbb{C}:\left|z\right|.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

scholarly journals Chebyshev Polynomials for Certain Subclass of Bazilevic Functions Associated with Ruscheweyh Derivative

2021 ◽  
Vol 45 (02) ◽  
pp. 173-180
Author(s):  
A. R. S. JUMA ◽  
S. N. AL-KHAFAJI ◽  
O. ENGEL
Keyword(s):  
Chebyshev Polynomials ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Bazilevic Functions

In this paper, through the instrument of the well-known Chebyshev polynomials and subordination, we defined a family of functions, consisting of Bazilević functions of type α, involving the Ruscheweyh derivative operator. Also, we investigate coefficient bounds and Fekete-Szegö inequalities for this class.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

scholarly journals Inclusion and neighborhood properties of a certain subclasses of p-valent functions with negative coefficients

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 1-13 ◽  
Author(s):  
R.M. El-Ashwah
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Function Class ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Inclusion Relations

By means of Ruscheweyh derivative operator, we introduced and investigated two new subclasses of p-valent analytic functions. The various results obtained here for each of these function class include coefficient bounds and distortion inequalities, associated inclusion relations for the (n, ?)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of non-homogenous differential equation.

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 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 Coefficient Estimates for Some Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Linear Operator

2021 ◽  
Vol 20 ◽  
pp. 115-120
Author(s):  
Dhirgam Allawy Hussein Hussein ◽  
Sahar Jaafar Mahmood
Keyword(s):  
Linear Operator ◽  
General Formula ◽  
Univalent Function ◽  
Symmetric Function ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Analytical Functions

 The articles introduces and investigates "two new subclasses of the bi-univalent functions ." These are analytical functions related to the m-fold symmetric function  and  .   We calculate the initial coefficients for all the functions that belong to them, as well as the coefficients for the functions that belong to a field where finding these coefficients requires a complicated method. Between the remaining results, the upper bounds for "the initial coefficients  "are found in our study as well as several examples. We also provide a general formula for the function and its inverse in the m-field. A function is called analytical if it does not take the same values twice .  It is called a univalent function if it is analytical at all its points, and the function is called a bi-univalent if it and its inverse are univalent functions together. We also discuss other concepts and important terms.   .

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