Pranay Goswami, Badr Alkahtani, Teodor Bulboaca
In this paper, estimates for second and third MacLaurin coefficients of certain subclasses of bi-univalent functions in the open unit disk defined by convolution are determined, and certain special cases are also indicated. The main result extends and improve a recent one obtained by Srivastava et al.
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In this paper we introduce and investigate two new subclasses of the function class $Σ$ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-MacLaurin coefficients $|a_2|$ and $|a_3|$ for functions in these new subclasses. Several known or new consequences of these results are also pointed out.
Our objective in this paper is to introduce and investigate comprehensive-constructed subclasses of normalized analytic and bi-univalent functions on the unit open disc. Bounds for the second and third Tayler-Maclaurin coefficients of functions belonging to this subclasses were investigated. Furthermore, some improvement and connections to some of the previous known results are also pointed out.
In the present paper, we investigate connections between various subclasses of harmonic univalent functions by using a convolution operator involving the Pascal distribution series.
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notion of harmonic Alexander integral operator is introduced. Also, the radius of convexity for certain families of harmonic functions is determined.
In the present investigation, we consider two new subclasses N_{Σ}^{μ}(α,λ) and N_{Σ}^{μ}(β,λ) of bi-univalent functions defined in the open unit disk U={z:|z|<1}. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.
The purpose of the present paper is to find the necessary and 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 $\mathbb{D}.$ Further, we consider the properties of integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.
In this paper we determine the disks $|z|<r\le1$ where for different classes of univalent functions, we have the property $${\rm Re}\left\{2\frac{zf'(z)}{f(z)}-\frac{z f''(z)}{f'(z)}\right\}>0\qquad (|z|<r).$$
In this work, we introduce two new subclasses S_{Σ_{m}}(α,λ) and S_{Σ_{m}}(\b{eta},λ) of Σ_{m} consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. Furthermore, for functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for |a_{m+1}| and |a_{2m+1}|.
In this paper our purpose is to find upper bound estimate for the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for functions defined by convolution belonging to the class $\mathcal{N}_σ^{μ,δ}(λ,t)$ by using Chebyshev polynomials.
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.
Some $m$-Fold Symmetric Bi-Univalent Function Classes and Their Associated Taylor-Maclaurin Coefficient Bounds
本文利用Ruscheweyh导数算子引入$m$重对称双单叶函数的一般子类，获得初始Taylor-Maclaurin系数界并改进现有结果，同时探讨了这些数学概念在光学设计、信号处理等工程领域的应用价值。
Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), and Caglar et al. (2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and bi-univalent functions in the open unit disk U. For functions belonging to these general subclasses introduced here, we obtain estimates on the Taylor-Maclaurin coefficients |a_2| and |a_3|. Several connections to some of the earlier known results are also pointed out. The results presented in this paper would generalize and improve those in related works of sev…
Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^σ\colon A\to A$ using the convolution *. Using these operators, we define and study new classes of functions in the unit disk. Moreover, we obtain some basic properties of the new classes, namely inclusion, growth, covering, distortion, closure under certain integral transformation and coefficient inequalities.
Radii of Concavity for Subclasses of Univalent Functions Associated with the Exponential Mapping
本文在Avkhadiev--Wirths几何框架下，通过显式超越方程刻画了与指数映射相关的单叶函数类的凹性半径，构造极值函数证明全局尖锐性，并数值验证了半径关于参数A的严格单调性。
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.
Estimates for initial coefficients of Taylor-Maclaurin series of bi-univalent functions belonging to certain classes defined by subordination are obtained. Our estimates improve upon the earlier known estimates for second and third coefficient. The bound for the fourth coefficient is new. In addition, bound for the fifth coefficient is obtained for bi-starlike and strongly bi-starlike functions of order $ρ$ and $β$ respectively.
Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third Taylor-Maclaurin coefficients, and also Fekete-Szego inequalities of functions belonging to this subclass are founded. Several connections to some of the earlier known results are also pointed out.
A univalent meromorphic function defined on $Δ:= \{z \in \mathbb{C}: 1<|z|<\infty \}$ with univalent inverse defined on $Δ$ is bi-univalent meromorphic in $Δ$. For certain subclasses of meromorphic bi-univalent functions, estimates on the initial coefficients are obtained.
For a real constant $b,$ we give sharp estimates of $\log|f(z)/z|+b\arg[f(z)/z]$ for subclasses of normalized univalent functions $f$ on the unit disk.
In this paper, we introduce and investigate a new subclass of the function class $Σ$ of bi-univalent functions defined in the open unit disk, which are associated with the Sălăgean type $q-$ difference operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in the new subclass introduced here. Several (known or new) consequences of the results are also pointed out. Further we obtain Fekete-Szeg$\ddot{o}$ inequality for the new function class.
The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Touchard polynomials. To be more precise, we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk U.
In this paper we determine the region of variability for certain subclasses of univalent functions satisfying differential inequalities. In the final section we graphically illustrate the region of variability for several sets of parameters.
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.
Introducing a new method we give sharp estimates of the Hermitian Toepliz determinants of third order for the class $\mathcal{S}$ of functions univalent in the unit disc. The new approach is also illustrated on some subclasses of the class $\mathcal{S}$.
Sharp upper and lower bounds for the second and third order Hermitian-Toepilitz determinants are obtained for some generalized subclasses of starlike and convex functions. Applications of these results are also discussed for several widely known classes.
In this paper by making use of the generalized Bernardi - Libera - Livingston integral operator we introduce and study some new subclasses of univalent functions. Also we investigate the relations between those classes and the classes which are studied by Jin-Lin Liu.
Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent functions. The bounds obtained improve some existing known bounds.
An analytic function $f$ defined on the open unit disk $\mathbb{D}=\{z:|z|<1\}$ is bi-univalent if the function $f$ and its inverse $f^{-1}$ are univalent in $\mathbb{D}$. Estimates for the initial coefficients of bi-univalent functions $f$ are investigated when $f$ and $f^{-1}$ respectively belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.
By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions is evident in the results obtained.
The purpose of the present paper is to introduce a new subclasses of the function class of bi-univalent functions defined in the open unit disc. Furthermore, we obtain estimates on the coefficients $|a_{2}|$ and $|a_{3}|$ for functions of this class. Some results related to this work will be briefly indicated.
By considering a fixed point in unit disk $Δ$, a new class of univalent convex functions is defined. Coefficient inequalities, integral operator and extreme points of this class are obtained.
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…
The object of this paper is to study relationship between successive coefficients of some subclasses of the class of univalent functions in the unit disk. the result obtained is sharp, and is used to provide a new, short proof of the well-known conjecture of Robertson on the coefficients of close-to-convex functions.
We consider a family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. The aim of this article is to investigate the bounds of the difference of moduli of initial successive coefficients, i.e. $\big | |a_{n+1}|-|a_n|\big |$ for $n=1,\,2$ and for some subclasses of analytic univalent functions. We found that all the estimations are sharp in nature by constructing some extremal functions.
Omitted values for some subclasses of univalent mappings
本文研究了某些单值映射子类的遗漏值问题，引入了完全凸映射类CC_α，并推广了经典结果。
Univalent Functions involving Generalized Hypergeometric Series
本文研究广义超几何级数与开单位圆盘内具有正泰勒系数的正规化解析函数子类之间的关联，建立两者间的相互联系。
We give some coefficient bounds and distortion theorems for a subclass of univalent functions in the unit disk, and defined using the Sâlâgean differential operator. The results generalize and unify some well known results for several subclasses of univalent functions defined on the unit disk having form $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$, normalized such that $f(0)=0$ and $f^\prime(0)=1$.
Let $\mathcal{S}$ denote the family of all functions that are analytic and univalent in the unit disk $\mathbb{D}:=\{z: |z|<1\}$ and satisfy $f(0)=f^{\prime}(0)-1=0$. In the present paper, we consider certain subclasses of univalent functions associated with the exponential function, and obtain the sharp upper bounds on the initial coefficients and the difference of initial successive coefficients for functions belonging to these classes.
On the symmetric $q$-analog on the bi-univalent functions with respect to symmetric points
本研究引入并探究了与对称$q$-导数算子、广义Bernardi积分算子相关的双单叶函数新子类，推导了约简子类的第二类Hankel行列式、Fekete-Szegö泛函不等式及系数上界。
Let $\mathcal{S}$ denote the class of analytic and univalent functions in $\mathbb{D}:=\{z\in\mathbb{C}:\, |z|<1\}$ of the form $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$. In this paper, we determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in $\mathcal{S}$ and its certain subclasses. We also discuss similar problems for typically real functions.
We consider functions of the type $f(z)=z+a_2z^2+a_3z^3+\cdots$ from a family of all analytic and univalent functions in the unit disk. Let $F$ be the inverse function of $f$, given by $F(z)=w+\sum_{n=2}^{\infty}A_nw^n$ defined on some $|w|\le r_0(f)$. In this paper, we find the sharp bounds of $\big | |A_{n+1}|-|A_n|\big |$, for $n=1,\,2$, for some subclasses of univalent functions.
A starlike univalent function $f$ is characterized by the function $zf'(z)/f(z)$; several subclasses of these functions were studied in the past by restricting the function $zf'(z)/f(z)$ to take values in a region $Ω$ on the right-half plane, or, equivalently, by requiring the function $zf'(z)/f(z)$ to be subordinate to the corresponding mapping of the unit disk $\mathbb{D}$ to the region $Ω$. The mappings $w_1(z):=z+\sqrt{1+z^2}, w_2(z):=\sqrt{1+z}$ and $w_3(z):=e^z$ maps the unit disk $\mathbb{D}$ to various regions in the right half plane. For normalized analytic functions $f$ satisfying th…
A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to be in certain subclasses of functions are established in terms of the Schwarzian derivatives and the second coefficients. These include obtaining a sufficient condition for functions to be strongly $α$-Bazileviĉ of order $β$.
Certain subclass of harmonic functions associated with univalent functions
该研究定义了一类与满足微分不等式的解析函数相关的保向调和函数子类，建立了两类函数的关联，推导了该子类的多种特征性质，并给出了特殊函数与调和单叶多项式属于该子类的条件。
We consider three classes of functions defined using the class $\mathcal{P}$ of all analytic functions $p(z)=1+cz+\dotsb$ on the open unit disk having positive real part and study several radius problems for these classes. The first class consists of all normalized analytic functions $f$ with $f/g\in\mathcal{P}$ and $g/(zp)\in\mathcal{P}$ for some normalized analytic function $g$ and $p\in \mathcal{P}$. The second class is defined by replacing the condition $f/g\in\mathcal{P}$ by $|(f/g)-1|<1$ while the other class consists of normalized analytic functions $f$ with $f/(zp)\in\mathcal{P}$ for s…
In this study, a subclass of an univalent function with negative coefficients which is defined by a new general Linear operator have been introduced. The sharp results for coefficients estimators, distortion and closure bounds, Hadamard product, and Neighborhood, and this paper deals with the utilizing of many of the results for classical hypergeometric function, where there can be generalized to m-hypergeometric functions. A subclasses of univalent functions are presented, and it has involving operator which generalizes many well-known. Denote A the class of functions f and we have other resu…
Our present investigation is motivated essentially by the fact that, in Geometric Function Theory, one can find many interesting and fruitful usages of a wide variety of special functions and special polynomials. The main purpose of this article is to make use of the Horadam polynomials and the generating function, in order to introduce three new subclasses of the bi-univalent function class. For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete Szego inequalities. Some interesting observations of the results presented here are also discussed. W…
In the present article, our goal is finding estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for a new class of bi-univalent functions defined by means of the Horadam polynomials. Fekete-Szego inequalities of functions belonging to this subclass are also founded.
Let $\mathcal{S}$ denote the class of functions analytic and univalent (i.e. one-to-one) in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:\, |z|<1\}$ normalized by $f(0)=0=f'(0)-1$. The logarithmic coefficients $γ_n$ of $f\in\mathcal{S}$ are defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty} γ_n z^n.$ In the present paper, we determine the sharp upper bounds for $|γ_1|$, $|γ_2|$ and $|γ_3|$ when $f$ belongs to some familiar subclasses of close-to-convex functions.
Making use of the Hadamard product(or convolution), we find some estimates on the Taylor-Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ for functions belong to bi univalent functions of the Bazilevi$\check{c}$ type of order $γ$. Several (known or new) consequences of the results are also pointed out.
This paper makes a modest contribution to the family of starlike univalent mappings in the open unit disk, by the introduction of some new subclasses of them via certain convolution operators. A new univalence condition is given with examples. Some basic characterizations of functions of the new subclasses are also mentioned.
The principal goal of this paper is to extend the classical problem of find the values of $α\in \C$ for which the mappings, either $F_α(z)=\int_0^z(f(ζ)/ζ)^αdζ$ or $f_α(z)=\int_0^z(f'(ζ))^αdζ$ are univalent, whenever $f$ belongs to some subclasses of univalent mappings in $\D$, but in the case of harmonic mappings, considering the \textit{shear construction} introduced by Clunie and Sheil-Small in \cite{CSS}.
Moduli difference of inverse logarithmic coefficients of univalent functions
本文研究了单值函数类中逆对数系数的模差界，确定了第二和第一逆对数系数的精确上界和下界。
Univalence of horizontal shear of Cesàro type transforms
本文研究Cesàro型变换的参数条件使其在单位圆盘内保持单叶性，推导对应调和映射及其旋转的单叶特征，给出非平凡单叶调和映射实例，采用Becker准则与剪切构造法作为核心工具。
In this paper, we introduce and investigate a new subclass of the function class $Σ$ of bi-univalent functions defined in the open unit disk, which are associated with the Hurwitz-Lerch zeta function, satisfying quasi-subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in this new subclass. Several (known or new) consequences of the results are also pointed out.
On Hardy spaces, univalent functions and the second coefficient
本文研究具有指定第二Taylor系数的单叶函数，给出了凸函数及其导数所属Hardy空间的尖锐估计，并扩展了病态边界行为定理至任意第二系数。
A geometric investigation of a certain subclass of univalent functions
本文研究了单值函数子类M(λ)的半径性质及关联结果，确定了函数F属于M类的最大圆半径，并得到特定星形函数的精确Bohr半径。
In this paper, two new subclasses of bi-univalent functions related to conic domains are defined by making use of symmetric $q$-differential operator. The initial bounds for Fekete-Szegö inequality for the functions $f$ in these classes are estimated.
On the Convexity of the Bernardi Integral Operator
该研究证明Bernardi积分算子可将特定有界星形函数类映射为凸函数类，改进了已有结果，并提出通用统一方法以研究其他多种保留单叶、p叶函数子类性质的积分算子。
We consider a family of all analytic and univalent functions (i.e., one-to-one) in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper, we obtain the sharp bounds of the second Hankel determinant of Logarithmic coefficients for some subclasses of analytic functions.
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