scholarly journals Coefficient Estimates for Bi-univalent Functions Defined By (P, Q) Analogue of the Salagean Differential Operator Related to the Chebyshev Polynomials

2021 ◽  
Vol 53 (1) ◽  
pp. 49-66
Author(s):  
Trailokya Panigrahi ◽  
Susanta Kumar Mohapatra
Keyword(s):  
Differential Operator ◽  
Univalent Function ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Coefficient Bounds ◽  
Varying Parameters ◽  
Function Classes ◽  
Sălăgean Operator ◽  
Salagean Operator

In the present investigation we use the Jackson (p,q)-differential operator to introduce the extended Salagean operator denoted by Rkp,q. Certain bi-univalent function classes based on operator Rkp,q related to the Chebyshev polynomials are introduced. First, two coefficient bounds and Fekete-Szego inequalities for the function classes are established. A number of corollaries are developed by varying parameters involved.

scholarly journals Coefficient Bounds for Subclasses of Biunivalent Functions Associated with the Chebyshev Polynomials

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Hatun Özlem Güney ◽  
G. Murugusundaramoorthy ◽  
K. Vijaya
Keyword(s):  
Unit Disk ◽  
Chebyshev Polynomials ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Function Classes ◽  
Sălăgean Operator ◽  
Salagean Operator

We introduce and investigate new subclasses of biunivalent functions defined in the open unit disk, involving Sălăgean operator associated with Chebyshev polynomials. Furthermore, we find estimates of the first two coefficients of functions in these classes, making use of the Chebyshev polynomials. Also, we give Fekete-Szegö inequalities for these function classes. Several consequences of the results are also pointed out.

scholarly journals On coefficient inequalities of certain subclasses of bi-univalent functions involving the Sălăgean operator

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1305-1313
Author(s):  
Amol Patil ◽  
Uday Naik
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Coefficient Inequalities

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.

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 Development of Novel Subclasses for Bi-Univalent Functions

2021 ◽  
Vol 16 ◽  
pp. 1-6
Author(s):  
MUNIRAH ROSSDY ◽  
RASHIDAH OMAR ◽  
SHAHARUDDIN CIK SOH
Keyword(s):  
Differential Operator ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Initial Coefficient

This manuscript presents the development of new subclasses for bi-univalent functions and the subclasses are closely related to Chebyshev polynomials having Al-Oboudi differential operator. The functions contained in the subclasses were used to account for the initial coefficient estimates of |a2| and |a3| .

scholarly journals A Subclass of Bi-Univalent Functions Defined by Generalized Sãlãgean Operator Related to Shell-Like Curves Connected with Fibonacci Numbers

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Gurmeet Singh ◽  
Gurcharanjit Singh ◽  
Gagandeep Singh
Keyword(s):  
Differential Operator ◽  
Fibonacci Numbers ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Sălăgean Operator ◽  
Salagean Operator

The aim of this paper is to study certain subclasses of bi-univalent functions defined by generalized Sãlãgean differential operator related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients a2 and a3 and upper bounds for the Fekete-Szegö functional for the functions in this class. The results proved by various authors follow as particular cases.

scholarly journals On univalent functions with negative coefficients by using generalized Sâlâgean operator

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Rahman Juma ◽  
S.R. Kulkarni
Keyword(s):  
Hadamard Product ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Sălăgean Operator ◽  
Salagean Operator

In this paper we have introduced a subclass AR(n, ?, ?, ?, ?) of univalent functions with negative coefficients defined by Salagean operator D?. We have obtained sharp results for coefficient estimates, distortion and closure bounds, Hadamard product and other results. .

scholarly journals On univalent functions defined by a generalized Sălăgean operator

2004 ◽  
Vol 2004 (27) ◽  
pp. 1429-1436 ◽  
Author(s):  
F. M. Al-Oboudi
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
Extreme Points ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Inclusion Relations ◽  
Convolution Properties

We introduce a class of univalent functionsRn(λ,α)defined by a new differential operatorDnf(z),n∈ℕ0={0,1,2,…}, whereD0f(z)=f(z),D1f(z)=(1−λ)f(z)+λzf′(z)=Dλf(z),λ≥0, andDnf(z)=Dλ(Dn−1f(z)). Inclusion relations, extreme points ofRn(λ,α), some convolution properties of functions belonging toRn(λ,α), and other results are given.

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