Faber Polynomial Coefficient Estimates for Bi-univalent Functions Defined by the Tremblay Fractional Derivative Operator

2018 ◽  
Vol 44 (1) ◽  
pp. 149-157 ◽  
Author(s):  
H. M. Srivastava ◽  
S. Sümer Eker ◽  
S. G. Hamidi ◽  
J. M. Jahangiri
Keyword(s):  
Fractional Derivative ◽  
Univalent Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Faber Polynomial

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 Faber Polynomial Coefficient Estimates for Meromorphic Bi-Starlike Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Samaneh G. Hamidi ◽  
Suzeini Abd Halim ◽  
Jay M. Jahangiri
Keyword(s):  
Univalent Functions ◽  
Starlike Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Faber Polynomial

We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent.

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

2017 ◽  
Vol 10 (01) ◽  
pp. 1750016 ◽  
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.

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

2018 ◽  
Vol 68 (2) ◽  
pp. 369-378 ◽  
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.

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

2015 ◽  
Vol 353 (2) ◽  
pp. 113-116 ◽  
Author(s):  
Serap Bulut ◽  
Nanjundan Magesh ◽  
Vittalrao Kupparao Balaji
Keyword(s):  
Univalent Functions ◽  
Polynomial Coefficient ◽  
Coefficient Estimates ◽  
Faber Polynomial
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