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

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.

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Coefficient bounds for M-fold symmetric analytic bi-Bazilevič functions using by Faber polynomial expansion

Creative Mathematics and Informatics ◽

10.37193/cmi.2020.01.10 ◽

2020 ◽

Vol 29 (1) ◽

pp. 81-89

Author(s):

F. MUGE SAKAR ◽

H. OZLEM GUNEY

Keyword(s):

Unit Disc ◽

Upper Bounds ◽

Polynomial Expansion ◽

Open Unit ◽

Coefficient Estimates ◽

Open Unit Disc ◽

Faber Polynomial ◽

Coefficient Bounds ◽

Polynomial Expansions ◽

Bazilevic Functions

A function is said to be bi-univalent in the open unit disc D, if both the function f and its inverse are univalent in the unit disc. Besides, a function is said to be bi-Bazilevic in ˘ D, if both the function f and its inverse are Bazilevic there. The behaviour of these types of functions are unpredictable ˘ and not much is known about their coefficients. In this study, we determined coefficient estimates for the Taylor Maclaurin coefficients of the class on m-fold symmetric bi-Bazilevic functions. We also, use the Faber Polynomial expansions to obtain these coefficient estimates associated with ˘ upper bounds.

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

Mathematics ◽

10.3390/math8020172 ◽

2020 ◽

Vol 8 (2) ◽

pp. 172 ◽

Cited By ~ 1

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.

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Faber polynomial coefficient estimates for a class of analytic bi-univalent functions involving a certain differential operator

Asian-European Journal of Mathematics ◽

10.1142/s1793557117500164 ◽

2017 ◽

Vol 10 (01) ◽

pp. 1750016 ◽

Cited By ~ 1

Author(s):

Poonam Sharma

Keyword(s):

Differential Operator ◽

Univalent Functions ◽

Polynomial Coefficient ◽

Coefficient Estimates ◽

Faber Polynomial

In this paper, we define a sub-class of analytic bi-univalent functions associated with a certain differential operator [Formula: see text]. Bounds for the general Taylor–Maclaurin coefficients [Formula: see text] for the functions in this class are obtained. Estimates for the coefficient [Formula: see text] and the estimate for the functional [Formula: see text] for any real [Formula: see text], are also found. Results for the specific values of the parameters [Formula: see text], are also given mentioning some of the results obtained earlier.

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Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

Mathematica Slovaca ◽

10.1515/ms-2017-0108 ◽

2018 ◽

Vol 68 (2) ◽

pp. 369-378 ◽

Cited By ~ 3

Author(s):

Ahmad Zireh ◽

Ebrahim Analouei Adegani ◽

Mahmood Bidkham

Keyword(s):

Unit Disk ◽

Univalent Functions ◽

Upper Bounds ◽

Polynomial Expansion ◽

Polynomial Coefficient ◽

Open Unit ◽

Open Unit Disk ◽

Coefficient Estimates ◽

Faber Polynomial

Abstract In this paper, we use the Faber polynomial expansion to find upper bounds for |an| (n ≥ 3) coefficients of functions belong to classes $\begin{array}{} H_{q}^{\Sigma}(\lambda,h),\, ST_{q}^{\Sigma}(\alpha,h)\,\text{ and} \,\,M_{q}^{\Sigma}(\alpha,h) \end{array}$ which are defined by quasi-subordinations in the open unit disk 𝕌. Further, we generalize some of the previously published results.

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

Asian-European Journal of Mathematics ◽

10.1142/s179355712050076x ◽

2019 ◽

Vol 13 (04) ◽

pp. 2050076 ◽

Cited By ~ 1

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.

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

Journal of Mathematical and Fundamental Sciences ◽

10.5614/j.math.fund.sci.2021.53.1.4 ◽

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.

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

Filomat ◽

10.2298/fil1606567b ◽

2016 ◽

Vol 30 (6) ◽

pp. 1567-1575 ◽

Cited By ~ 4

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.

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Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽

10.3390/axioms10010027 ◽

2021 ◽

Vol 10 (1) ◽

pp. 27

Author(s):

Hari Mohan Srivastava ◽

Ahmad Motamednezhad ◽

Safa Salehian

Keyword(s):

Unit Disk ◽

Univalent Functions ◽

Expansion Method ◽

Upper Bounds ◽

Polynomial Expansion ◽

Open Unit ◽

Open Unit Disk ◽

Faber Polynomial ◽

The Subject ◽

Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

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