Inclusion properties for bi-univalent functions of complex order defined by combining of Faber polynomial expansions and Fibonacci numbers

Sahsene Altinkaya, Samaneh G. Hamidi, Jay M. Jahangiri, Sibel Yalcin

英文摘要：

In this present investigation, we introduce the new class R of bi-univalent functions defined by using the Tremblay fractional derivative operator. Additionally, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general coefficient an of the bi-univalent function class.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

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

In the present paper, we were mainly concerned with obtaining estimates for the general Taylor-Maclaurin coefficients for functions in a certain general subclass of analytic bi-univalent functions. For this purpose, we used the Faber polynomial expansions. Several connections to some of the earlier known results are also pointed out.

2018-10-14math.CV

Faber polynomial coefficient estimation of subclass of bi-subordinate univalent functions

In this paper, a comprehensive subclass of bi-univalent functions class are introduced and investigated. Using the Faber polynomials, estimation of the coefficients $|a_n|$ and certain Fekete-Szegö inequality of Maclaurin expansion of functions in this subclass are concluded. Finally, some earlier results are pointed out and improved.

2022-02-24math.CV

Initial estimates for certain subclasses of bi-univalent functions with $κ-$Fibonacci numbers

In this work, we consider certain class of bi-univalent functions related with shell-like curves related to $κ-$Fibonacci numbers. Further, we obtain the estimates of initial Taylor-Maclaurin coefficients (second and third coefficients) and Fekete - Szegö inequalities. Also we discuss the special cases of the obtained results.

2020-01-22math.CV

Certain classes of bi-univalent functions related to Shell-like curves connected with Fibonacci numbers

Recently, in their pioneering work on the subject of bi-univalent functions, Srivastava et al. \cite{HMS-AKM-PG} actually revived the study of the coefficient problems involving bi-univalent functions. Inspired by the pioneering work of Srivastava et al. \cite{HMS-AKM-PG}, there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions. Motivated largely by Ali et al. \cite{Ali-Ravi-Ma-Mina-class}, Srivastava et al. \cite{HMS-AKM-PG} and Güney et al. \cite{HOG-GMS-JS-Fib-2018} in this paper, we consider certain classes of bi-univalent…

2018-10-15math.CV

A Comprehensive subclass of analytic and bi-univalent functions associated with subordination

In the present paper, we define a new general subclass of bi-univalent functions involving a differential operator in the open unit disk U. For this purpose, we use the Faber polynomial expansions. Several connections to some of the earlier known results are also pointed out.

2018-11-16math.CV

Faber Polynomials with common zero

We describe the two sets of meromorphic univalent functions in the class $Σ$, for which the sequence of Faber polynomials $\{F_j\}_{j=1}^\infty $ have the roots with following properties respectively: $\sum_{j=1}^{n}|F_j(z_0)|=0<|F_{n+1}(z_0)|, $ $n\in\mathbb N, $ and $|F_1(z_0)|> 0=\sum_{j=2}^{\infty}|F_j(z_0)|$. We found an explicit form of Faber polynomials for such functions.

2015-05-10math.CV

更多相关论文收起更多论文

具有分段解析边界区域的Faber多项式的渐近性

On the asymptotic behavior of Faber polynomials for domains with piecewise analytic boundary

对于{w：1< |w| < \infty }中解析的单叶函数g（w），在\infty上有一个单极点，并且是{w：|w| \geq 1}的连续扩张，我们考虑Faber多项式F_n（z），n= 0，1，2，.，通过它们的生成函数g ′（w）/（g（w）-z）= \sum_{n=0}^\ infty F_n（z）w^{-（n+1）}与g（w）相关联。假设g（w）将单位圆T映射到一条外区域没有外尖点的分段解析曲线L上，并在关于g（w）关于T映射到L的角点的“Lehman展开式”的附加假设下，得到了F_n（z）的渐近公式，得到了关于Faber多项式零点的位置、极限分布和聚点的精确结果.渐近公式一致，并提供了确切的衰减率的误差项。

2007-06-13math.CAmath.CV