scholarly journals Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 147
Author(s):  
Ala Amourah ◽  
Basem Aref Frasin ◽  
Morad Ahmad ◽  
Feras Yousef
Keyword(s):  
Univalent Functions ◽  
Symmetric Domain ◽  
Gegenbauer Polynomials ◽  
Functional Problem ◽  
Pascal Distribution

In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, we provide estimates of Taylor–Maclaurin coefficients a2 and a3 for functions in the aforementioned class, and next, we solve the Fekete–Szegö functional problem. Moreover, some interesting findings for new subclasses of analytic bi-univalent functions will emerge by reducing the parameters in our main results.

scholarly journals ON BRANNAN'S COEFFICIENT CONJECTURE AND APPLICATIONS

2007 ◽  
Vol 49 (1) ◽  
pp. 45-52 ◽  
Author(s):  
STEPHAN RUSCHEWEYH ◽  
LUIS SALINAS
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Boundary Point ◽  
Univalent Functions ◽  
Gegenbauer Polynomials ◽  
Gauss Hypergeometric Function ◽  
Coefficient Estimates ◽  
Image Position

Abstract.D. Brannan's conjecture says that for 0 <α,β≤1, |x|=1, and n∈N one has |A2n−1(α,β,x)|≤|A2n−1(α,β,1)|, where We prove this for the case α=β, and also prove a differentiated version of the Brannan conjecture. This has applications to estimates for Gegenbauer polynomials and also to coefficient estimates for univalent functions in the unit disk that are ‘starlike with respect to a boundary point’. The latter application has previously been conjectured by H. Silverman and E. Silvia. The proofs make use of various properties of the Gauss hypergeometric function.

Certain subclasses of univalent functions involving Pascal distribution series

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Abdel Moneim Y. Lashin ◽  
Abeer O. Badghaish ◽  
Amani Z. Bajamal
Keyword(s):  
Univalent Functions ◽  
Pascal Distribution

scholarly journals Certain subclasses of Spiral-like univalent functions related with Pascal distribution series

2021 ◽  
Vol 7 (2) ◽  
pp. 312-323
Author(s):  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Inclusion Relations ◽  
Pascal Distribution

Abstract The purpose of the present paper is to find the sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations for such subclasses in the open unit disk 𝔻. Further, we consider the properties of integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

scholarly journals New Families of Bi-Univalent Functions Governed by Gegenbauer Polynomials

2021 ◽  
pp. 403-427
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Univalent Functions ◽  
Gegenbauer Polynomials ◽  
Do So

The aim of this article is to initiating an exploration of the properties of bi-univalent functions related to Gegenbauer polynomials. To do so, we introduce a new families \mathbb{T}_\Sigma (\gamma, \phi, \mu, \eta, \theta, \gimel, t, \delta) and \mathbb{S}_\Sigma (\sigma, \eta, \theta, \gimel, t, \delta ) of holomorphic and bi-univalent functions. We derive estimates on the initial coefficients and solve the Fekete-Szeg problem of functions in these families.

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta
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