A new class of Salagean-type harmonic univalent functions

We define and investigate a new class of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convex combination and radii of convex for the above class of harmonic univalent functions.     

Faber polynomials with applications to univalent functions with quasiconformal extensions

We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l ² space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.     

Meromorphic univalent functions in an annulus

We consider the integral means for the class of functions which are meromorphic and univalent in an annulus.     

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.

     

Uniformly locally univalent functions and Hardy spaces

We consider the class of uniformly locally univalent functions on the unit disk with prescribed pre-Schwarzian norm. In the present paper, we show that the class is contained in the Hardy space of a specific exponent depending on the norm.     

The fifth coefficient for bounded univalent functions with real coefficients

All stationary values of the fifth coefficient of bounded univalent functions with real coefficients are found, including maximum and minimum values.     

On a variational method for univalent functions

In the paper, the construction of a variational method for univalent functions is suggested; this construction uses the factorization theorem. As a consequence, an analog of the Goluzin variational formula is obtained.     

Convolution properties of some classes of meromorphic univalent functions

Convolution technique and subordination theorem are used to study certain class of meromorphic univalent functions in the punctured unit disc.     

Quasi-Hadamard product of certain univalent functions

The author improves some recent results due to Shigeyoshi Owa (Tamkang J. Math., 14 1983, 15–21) concerning the quasi-Hadamard product of certain starlike and convex univalent functions.     

Boundedness properties of univalent functions with positive coefficients

The present contribution investigates sharp lower bounds of the real parts of certain types of rational functions defined in terms of functions which are analytic and univalent in the open unit disk, and which also involve the familiar fractional derivative operator. Some worthwhile consequences of the main results are also pointed out.     

On the univalence of derivatives of functions which are univalent in angular domains

We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f ^(k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane.     

An estimate of the curvature of level curves in a class of univalent functions

In this note a class of normalized functions which are univalent in the unit disk is considered. An exact solution of the problem of an upper estimate of curvature of level curves for functions of this class is obtained. In particular, an exact solution of this problem for univalent functions with real coefficients at the points of the interval (0, 1) is obtained.Translated from Matematicheskie Zametki, Vol. 19, No. 3, pp. 381–388, March, 1976.The author is thankful to the referee for taking interest in this note.     

Application of generalized Hadamard product on special classes of analytic univalent functions

In this paper, the author established certain results concerning the quasi-Hadamard product for generalized subclasses of univalent functions with positive coefficients.     

Smale's mean value conjecture and the coefficients of univalent functions

We study Smale's mean value conjecture and its connection with the second coefficients of univalent functions. We improve the bound on Smale's constant given by Beardon, Minda and Ng.

     

The Hadamard product of meromorphic univalent functions defined by using convolution

In this work the authors extend certain results concerning the Hadamard product for two classes related to starlike and convex univalent meromorphic functions with positive coefficients by using convolution.     

关于单叶函数中几个结果的注记

首先就Mbius变换在几何函数论上应用时存在的两个误区予以讨论,指出其存在的问题与如何改正;其次明确地指出用Baernstein方法估计m次对称单叶函数之逆函数系数时的不足之处;最后就S ingh与Puri一文中的一个结果给以改正,并用Ruschew eyh的共轭方法得到该结果成立的最佳范围.     

The integral means spectrum of univalent functions

This is a survey of recent results on integral means of derivatives of univalent functions. Bibliography: 21 titles.Dedicated to the memory of Professor G. M. GoluzinTranslated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 119–128.     

Quasi-Hadamard product of a generalized class of analytic and univalent functions

In this paper, we introduce new subclasses of analytic and univalent functions and establish certain results concerning the quasi-Hadamard product of functions in these subclasses. Our result includes several previous known results as special cases.     

On the Fekete-Szegö problem for concave univalent functions

We consider the Fekete-Szegö problem with real parameter λ for the class Co(α) of concave univalent functions.     

Asymptotic estimates for the coefficients of bounded univalent functions

In the class of univalent bounded normalized holomorphic functions in the unit disk, we give an asymptotic estimate for the coefficients when the uniform norm of the modulus of the function tends to infinity.