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

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