The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator

被引：66

作者：

Srivastava, Hari Mohan ^{[1
,2
]}

Khan, Shahid ^{[3
]}

Ahmad, Qazi Zahoor ^{[4
]}

Khan, Nazar ^{[4
]}

Hussain, Saqib ^{[5
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[3] Riphah Int Univ, Dept Math, Islamabad, Pakistan

[4] Abbottabad Univ Sci & Technol, Dept Math, Abbottabad, Pakistan

[5] COMSATS Inst Informat Technol, Dept Math, Abbottabad, Pakistan

来源：

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA | 2018年 / 63卷 / 04期

关键词：

Analytic functions; univalent functions; Taylor-Maclaurin series representation; Faber polynomials; bi-inivalent functions; q-derivative operator; q-hypergeometric functions; q-integral operators;

D O I：

10.24193/subbmath.2018.4.01

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In our present investigation, we first introduce several new subclasses of analytic and bi-univalent functions by using a certain q-integral operator in the open unit disk U = {z : z is an element of C and vertical bar z vertical bar < 1}. By applying the Faber polynomial expansion method as well as the q-analysis, we then determine bounds for the nth coefficient in the Taylor-Maclaurin series expansion for functions in each of these newly-defined analytic and bi-univalent function classes subject to a gap series condition. We also highlight some known consequences of our main results.

引用

页码：419 / 436

页数：18

共 32 条

[31] Sharp Bounds of the Fekete-Szego Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limacon Domain
Shaba, Timilehin Gideon
Araci, Serkan
Adebesin, Babatunde Olufemi
Tchier, Fairouz
Zainab, Saira
Khan, Bilal
FRACTAL AND FRACTIONAL, 2023, 7 (07)
[32] Certain subclasses of λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}-pseudo bi-univalent functions with respect to symmetric points associated with the Gegenbauer polynomial
Adnan Ghazy Al Amoush
Gangadharan Murugusundaramoorthy
Afrika Matematika, 2023, 34 (1)

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