Estimates for Integral Means of Hyperbolically Convex Functions

We prove the Mejia-Pommerenke conjecture that the Taylor coefficients of hyperbolically convex functions in the disk behave like O(log^?2(n)/n) as n → ∞ assuming that the image of the unit disk under such functions is a domain of bounded boundary rotation. Moreover, we obtain some asymptotically sharp estimates for the integral means of the derivatives of such functions and consider an example of a hyperbolically convex function that maps the unit disk onto a domain of infinite boundary rotation.     

I族函数的反函数系数的精确上界

本文得出导数具有正实部的解折函数族的反函数的系数的精确上界。     

A linear operator associated with the Mittag-Leffer function and related conformal mappings

In the present paper, we introduce a linear operator associated with the Mittag-Leffler function. Some convolution properties of meromorphic functions involving this operator are given.     

Certain geometric properties of the Mittag-Leffler functions

In the present investigation, the Mittag-Leffler functions with their normalization are considered. Several sufficient conditions are obtained so that the Mittag-Leffler functions have certain geometric properties including univalency, starlikeness, convexity and close-to-convexity in the open unit disk. Partial sums of Mittag-Leffler functions are also studied. The results obtained are new and their usefulness is depicted by deducing several interesting corollaries and examples.     

Boundary Behavior in a Stolz Angle of Analytic Functions on the Disk

In this paper, we study the behavior of analytic functions (on the disk) in a Stolz angle. In particular, we prove assertions of the type of the Hardy--Littlewood theorem and obtain estimates for the growth of functions in a Stolz angle.     

Some radius problems related to a certain subclass of analytic functions

For real parameters α and β such that 0≤α1β,we denote by S(α,β) the class of normalized analytic functions which satisfy the following two-sided inequality:αR(zf′(z)/f(z))β,z∈U,where U denotes the open unit disk.We find a sufficient condition for functions to be in the class S(α,β) and solve several radius problems related to other well-known function classes.     

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.     

Sequentially Complete Inductive Limits and Regularity

A notion of an almost regular inductive limits is introduced. Every sequentially complete inductive limit of arbitrary locally convex spaces is almost regular.     

Subordination and superordination properties for a class of integral operators

In the present paper, we obtain some subordination- and superordinatiompreserving properties of certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorems for these integral operators are also considered.     

星像与强星像的某些充分条件(英文)

本文研究了与某些新的函数表达式相关的一些微分不等式及一阶微分从属关系的问题.利用微分从属的方法,获得了一些新的函数星像性与强星像性的充分条件,推广和改进了已有的一些结果.     

Univalence and starlikeness of certain transforms defined by convolution of analytic functions

Let U(λ) denote the class of all analytic functions f in the unit disk Δ of the form f(z)=z+a₂z²+? satisfying the condition

     

Reflexivity of Inductive Limits

An inductive locally convex limit of reflexive topological spaces is reflexive iff it is almost regular.     

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.     

凸函数的次微分与微分中值定理的逆定理

利用凸函数的性质,证明了次微分情形下微分中值定理的逆定理.     

负系数单叶函数的一个新子族

本文引入了一类具有负系数的单叶函数族C_n(α),并且讨论了这类函数族精确的系数估计,偏差定理及闭包定理,推广了一些已有结果.     

指数凸函数的积分不等式及其在Gamma函数中的应用

仿对数凸函数的概念,给出指数凸函数的定义,并证明有关指数凸函数的几个积分不等式,作为应用,得到一个新的Kershaw型双向不等式.