Functions In Unit Disk Research Articles

Hyperbolically Lipschitz continuity, area distortion and coefficient estimates for -quasiconformal harmonic mappings of unit disk

UDC 517.51 We study the hyperbolically Lipschitz continuity, Euclidean and hyperbolic area distortion theorem, and coefficient estimate for the classes of -quasiconformal harmonic mappings from the unit disk onto itself.

ON THE UNIVALENCE OF A NEW INTEGRAL PERATOR

Motivated by the linear operator studied by the author in [2, 3], the author introduce and study a new general integral operator defined on the class of normalized analytic function in the unit disc. This operator is motivated by many researchers. With this operator univalence conditions for the normalized analytic function in the open unit disc are obtained. Indeed, the author present a few conditions of univalency for our integral operator. . Having the integral operator, there are interesting properties of normalized function in the unit disc for univalent conditions for an integral operator. In addition, the author also find some interesting corollaries on the class of normalized analytic of functions in the open unit disc.

Fekete-Szego coefficient for a general class of spirallike functions in unit disk

The aim of this paper is to give sharp bound for the Fekete-Szego coecient functional of normalized analytic functions f(z) dened on the open unit disk in the complex plane are derived for the general class of spirallike functions in unit disk.

The Borel directions of algebroidal function and its coefficient functions

In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.

On a new type of singular point for meromorphic functions in the open unit disk

In this note, we will confirm the existence of a new type of singular point of an admissible meromorphic function in the unit disk. This work is a counterpart of the result of a meromorphic function with order in the complex plane studied by W. C. Lin and S. Mori.

Factorization for bounded analytic functions in the unit disk and an application to prime ideals

We prove several factorization theorems for bounded analytic functions in the open unit disk and present a very simple new proof of two conjectures of Frank Forelli and the author on the structure of finitely generated, respectively countably generated prime ideals in $H^{\infty}$.

TWO REMARKS ON SCHWARZ FORMULA

This paper discusses two problems. Firstly the authors give the Schwarz formula for a holomorphic function in unit disc when the boundary value of its real part is in the class H of generalized functions in the sense of Hua. Secondly the authors use the classical Schwarz formula to give a new proof of the zero free region of the Riemann zeta-function.

A GENERALIZATION OF CARATHEODORY INERUALITY

Let H be a Hilbert space. and f(z) is an analytic function in unit disk, |f(z)|<1, then ||f′(A)||≤||I-f.(A)f(A)||1/2||I-F(A)f.(A)||1/21-||A||2where A is a proper contraction operator on H.