On successive coefficients of odd univalent functions

The relative growth of successive coefficients of odd univalent functions is investigated. We prove that a conjecture of Hayman is true.

     

On certain new subclass of close-to-convex functions

In the present paper, we introduce a new subclass of the class of close-to-convex functions. The subordination and inclusion relationship, and some coefficient inequalities, a sufficient condition for this class are provided. Furthermore, we obtain the distortion theorems. The results presented here would provide extensions of those given in earlier works.     

Sharp distortion theorems for some subclass of close-to-convex functions

For real A, B such that −1 ? B < A ? 1, we denote by R(A,B) the class of functions, such that f′ ? (1 + Az)/(1 + Bz). Sharp distortion results for functions from R_A,B are obtained.     

复阶近于凸函数的相邻系数

研究了单叶函数相邻系数模之差的增长问题.利用复分析中的一些初等方法,获得了复阶近于凸函数类的相邻系数模之差的估计,得到精确结果,推广了一些作者的相关结果.     

On k-uniformly close-to-convex functions of complex order

In this paper, we define and study some subclasses of analytic functions by using fractional derivative operator. Some interesting properties, coefficients problems and inclusion results of these classes are investigated. It is also shown that these classes are closed under convolution with convex functions and some applications are given.     

Starlike and close-to-convex functions defined by differential inequalities

We present new sufficient conditions for an analytic function to be close-to-convex and starlike, respectively. These conditions are easy to apply and can be used to obtain functions in these classes.     

On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points

In the present paper, the authors introduce two new subclasses of close-to-convex functions and of quasi-convex functions. The integral representations for functions belonging to these classes are provided, the convolution conditions, growth theorems, distortion theorems and covering theorems for these classes are also provided. The results obtained generalize some known results, and some other new results are obtained.     

Migration of zeros for successive derivatives of entire functions

It is shown that if is an entire function of order less than one, all of whose zeros are real, then the minimal root of is an increasing function of which accelerates as increases.

     

Classes of analytic functions associated with the Choi-Saigo-Srivastava operator

We investigate several properties of the linear Choi-Saigo-Srivastava operator and associated classes of analytic functions which were introduced and studied by J.H. Choi, M. Saigo and H.M. Srivastava [J.H. Choi, M. Saigo, H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002) 432-445]. Several theorems are an extension of earlier results of the above paper.     

Inclusion relations and convolution properties of a certain class of analytic functions associated with the Ruscheweyh derivatives

Let A denote the class of functions f(z) with

f(0)=f^′(0)−1=0,     

A sharp inequality for the logarithmic coefficients of univalent functions

We prove the sharp inequality

for the logarithmic coefficients of a normalized univalent function in the unit disk.

     

On the properties of a certain subclass of close-to-convex functions

In the present paper, we introduce an interesting subclass Kps (h)of analytic functions in the open unit disk U. For functions belonging to theclass Kps (h), basic properties such as the coefficient bounds, the distortionand growth theorems are derived. The results presented here would provideextensions of those given by Q.-H. Xu et al. [2].     

Some properties of certain meromorphic close-to-convex functions

In the present paper, we introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, distortion property and radius of meromorphic convexity are derived.     

On classes of analytic functions defined by convolution with incomplete beta functions

Carlson and Shaffer [SIAM J. Math. Anal. 15 (1984) 737-745] defined a convolution operator L(a,c) on the class A of analytic functions involving an incomplete beta function ?(a,c;z) as L(a,c)f=?(a,c)?f. We use this operator to introduce certain classes of analytic functions in the unit disk and study their properties including some inclusion results, coefficient and radius problems. It is shown that these classes are closed under convolution with convex functions.     

On the Faber coefficients of functions univalent in an ellipse

Let be the elliptical domain

Let denote the class of functions analytic and univalent in and satisfying the conditions and . In this paper, we obtain global sharp bounds for the Faber coefficients of the functions in certain related classes and subclasses of

     

The fekete-szegö problem for close-to-convex functions with respect to the koebe function

An analytic function f   in the unit disk D :={z ∈ ? : |z| < 1}$\mathbb{D}\hspace{0.17em}:=\left\{z\hspace{0.17em}\in \hspace{0.17em}?\hspace{0.17em}:\hspace{0.17em}\left|z\right|\hspace{0.17em}<\hspace{0.17em}1\right\}$, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1−z)², z ∈ D$k\left(z\right)\hspace{0.17em}:=\hspace{0.17em}z/{\left(1-z\right)}^2,\hspace{0.17em}z\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$ if there exists δ∈(-π/2,π/2) such that Re{eiδ(1−z)²f^′(z)} > 0, ∈ D$\text{Re}\left\{{\text{e}}^{\text{i}\delta }{\left(1-z\right)}^2{f}^{\prime }\left(z\right)\right\}\hspace{0.17em}>\hspace{0.17em}0,\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szegö problem is studied.     

Taylor coefficients of functions in Fock spaces

Analogues of the Hausdorff-Young and Hardy-Littlewood theorems are proved for functions in Fock spaces. Estimates of Taylor coefficients are shown to be sharp in the sense of Duren-Taylor.