亚纯p叶凸象函数的子类

本文引进单位圆盘内亚纯ｐ叶凸函数的新子类Ｃ（ｎ,ｐ,Ａ,Ｂ）和Ｋ（ｎ,ｐ,Ａ,Ｂ）,分别研究其包含关系与类中函数的积分变换等性质．     

Some subclasses of analytic functions with bounded Mocanu variation

Analytic functions with bounded Mocanu variation generalize the concept of α-convexity in the unit disc. We introduce and study certain classes of such functions. Inclusion results are obtained and a sharp radius problem is solved.     

On diameters of certain classes of functions analytic in the unit disc. II

Precise values are obtained for several diameters of certain function classes in the Orlicz space of functions analytic in the unit disc.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1019–1026, August, 1990.     

几个多复变数加权全纯函数空间的边界值与对偶性

该文将几个全纯函数空间的定义从单复变数推广到多复变数, 这些空间中全纯函数的增长性依赖于某个权函数. 作者研究了它们的增长性与边界值的关系以及这些空间相互之间的对偶关系, 所用方法和技巧与单复变数有不少区别. 所得到的结论是单复变数许多已知结果的推广.     

Partial differential subordinations and inequalities defined on complete circular domains

Let P:Cⁿ → C be holomorphic on a complete circular domain and let q be holomorphic and univalent on the unit disc U. The authors consider special classes of subordinations and inequalities involving partial derivatives of P. They show that if P satisfies these differential subordinations or inequalities, then P(Ω) c q(U). Applications of these results to partial differential inequalities, partial differential equations and harmonic functions are presented.     

A decomposition of functions with zero means on circles

It is well known that every Hölder continuous function on the unit circle is the sum of two functions such that one of these functions extends holomorphically into the unit disc and the other extends holomorphically into the complement of the unit disc. We prove that an analogue of this holds for Hölder continuous functions on an annulus A which have zero averages on all circles contained in A which surround the hole.     

Absolutely convex,uniformly starlike and uniformly convex harmonic mappings

In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disc. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings. A natural generalization of the classical Bernardi-type operator for harmonic functions is considered and its connection between certain classes of uniformly starlike harmonic functions and uniformly convex harmonic functions is also investigated. At the end, as applications, we present a number of results connected with hypergeometric and polylogarithm functions.     

Minimal area problems for functions with integral representation

We study the minimization problem for the Dirichlet integral in some standard classes of analytic functions. In particular, we solve the minimal areaa ₂-problem for convex functions and for typically real functions. The latter gives a new solution to the minimal areaa ₂-problem for the classS of normalized univalent functions in the unit disc. Supported by NSF grant DMS-0412908.     

Sandwich-type theorems for multivalent functions associated with the Srivastava-Attiya operator

In the present paper, we investigate some subordination- and superordination-preserving properties for certain classes of analytic and multivalent functions in the open unit disk, which are associated with such multiplier transformations as the Srivastava-Attiya operator. Various sandwich-type theorems for functions belonging to these classes are also obtained.     

Normality and boundary behaviour of arbitrary and meromorphic functions along simple curves and applications

In this paper, we establish some theorems giving necessary and sufficient conditions for an arbitrary function defined in the unit disc of the complex plane to have boundary values along classes of an equivalence relation over simple curves. Our results generalize the well-known theorems on asymptotic and angular boundary behaviours of meromorphic functions (Lindelölf-, Lehto–Virtanen- and Seidel–Walsh-type theorems). The obtained results are applied to the study of boundary behaviour of meromorphic functions along curves using P-sequences, as well as in the proof of the uniqueness theorem similar to ?aginjan’s one. The constructed examples of functions show that the results cannot be improved.     

Product of Schlicht functions

The class of regular schlicht functions in the unit disk and its subclasses of star-shaped convex functions are considered. New estimates for certain functionals in these classes and representations in the form of schlicht products, including the infinite ones, or different functions of the considered classes are obtained.Translated from Matematicheskie Zametki, Vol. 23, No. 5, pp. 697–708, May, 1978.     

On the Structure of Hv0(D) and hv0(D)

Weighted spaces of harmonic and holomorphic functions on the unit disc are discussed. It is shown that these spaces are always subspaces of c₀. Moreover, for many weights, it is shown that the weighted space of holomorphic functions has a basis.     

Löwner chains and a subclass of biholomorphic mappings

In this paper, we give characterization of almost starlike functions of order α (respectively almost starlike mappings of order α) on the unit disc in C (respectively the unit ball in a finite-dimensional complex Banach space) in terms of Löwner chains. Furthermore, using the properties of Löwner chains, we can easily prove that two classes of generalized Roper-Suffridge extension operators preserve almost starlikeness of order α on two important classes of Reinhardt domains in Cn, respectively.     

Some radii problems related to certain p-valent meromorphic functions

The purpose of the present paper is to introduce several new classes of p-valent meromorphic functions defined by Ruscheweyh derivative operator for meromorphic multivalent functions. Further, we investigate the radii problems of these analytic classes in the punctured unit disk.     

Some classes of analytic and multivalent functions involving a linear operator

By using a linear operator, which is defined here by means of the Hadamard product (or convolution), the authors introduce some new classes of analytic and multivalent functions in the open unit disk and investigate their inclusion relationships and convolution properties. Integral transforms of functions in these classes are also discussed.     

Harnack and Shmul’yan pre-order relations for Hilbert space contractions

We study the behavior of some classes of Hilbert space contractions with respect to Harnack and Shmul’yan pre-orders and the corresponding equivalence relations. We give some conditions under which the Harnack equivalence of two given contractions is equivalent to their Shmul’yan equivalence and to the existence of an arc joining the two contractions in the class of operator-valued contractive analytic functions on the unit disc. We apply some of these results to quasi-isometries and quasi-normal contractions, as well as to partial isometries for which we show that their Harnack and Shmul’yan parts coincide. We also discuss an extension, recently considered by S. ter Horst (2014), of the Shmul’yan pre-order from contractions to the operator-valued Schur class of functions. In particular, the Shmul’yan–ter Horst part of a given partial isometry, viewed as a constant Schur class function, is explicitly determined.     

The growth of solutions of differential equations with coefficients of small growth in the disc

In this paper, we classify the functions of small growth in the unit disc to different degree, and investigate the growth of solutions for certain linear differential equations with coefficients of small growth in the unit disc.     

利用微分算子定义的某类p-叶解析函数的一些基本性质（英文）

In this paper, we introduce new subclasses of p-valent analytic functions defined by using differential operator in the open unit disc. We study coefficient inequality, distortion theorem, radius of close to-convexity, starlikeness and convexity, extreme points and integral operator for functions in these new subclasses.