On a subclass of close-to-convex functions

We consider a subclass of the class of close-to-convex functions. We show the relationship between our class and the appropriate subordination. Moreover, we give the coefficient estimates and a sufficient condition for functions to belong to the class investigated. Finally, we obtain the distortion and the growth theorems. The results presented are a generalization of the results obtained by Gao and Zhou.     

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 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.     

On the successive coefficients of close-to-convex functions

Let f∈S, f be a close-to-convex function, f_k(z)=[f(z^k)]^1/k. The relative growth of successive coefficients of f_k(z) is investigated. The sharp estimate of ||c_n+1|−|c_n|| is obtained by using the method of the subordination function.     

The Noor integral operator and strongly close-to-convex functions

The purpose of the present paper is to introduce some new subclasses of strongly close-to-convex functions defined by using the Noor integral operator and study their inclusion relationships with the integral preserving properties. Our results include several previous known results as special cases.     

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 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.     

A generalization of a class of close-to-convex functions

We consider a class of functions, including the Bazilevich functions, which are regular in the unit disk. The theorems of Levandovskii identifying the class of close-to-convex functions with the class of linearly accessible functions are generalized, and the geometric structure of this class is established. A method constructing a subordinating homotopy chain is used.Translated from Matematicheskie Zametki, Vol. 11, No. 5, pp. 509–516, May, 1972.     

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.     

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.     

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].     

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.