Milloux Inequality of E

The main purpose of this paper is to establish the Milloux inequality of E-valued meromorphic function from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis. As an application, we study the Borel exceptional values of an E-valued meromorphic function and those of its derivatives; results are obtained to extend some related results for meromorphic scalar-valued function of Singh, Gopalakrishna, and Bhoosnurmath

Characteristic Functions and Borel Exceptional Values of E-Valued Meromorphic Functions

The main purpose of this paper is to investigate the characteristic functions and Borel exceptional values of E-valued meromorphic functions from the ℂR={z:|z|<R},   0<R≤+∞ to an infinite-dimensional complex Banach space E with a Schauder basis. Results obtained extend the relative results by Xuan, Wu and Yang, Bhoosnurmath, and Pujari

Filling Disks of Hayman Type of Meromorphic Functions

We obtain the existence of the filling disks with respect to Hayman directions. We prove that, under the condition limsupr→∞⁡(Tr,f/log⁡r3)=∞, there exists a sequence of filling disks of Hayman type, and these filling disks can determine a Hayman direction. Every meromorphic function of positive and finite order ρ has a sequence of filling disks of Hayman type, which can also determine a Hayman direction of order ρ

Some New Results on Fixed Points of Meromorphic Functions Defined in Annuli

The purpose of this paper is to investigate the fixed points of meromorphic functions in annuli. Some well-known facts of fixed points for meromorphic functions in the plane will be considered in annuli

Some New Inequalities on Laplace&ndash;Stieltjes Transforms Involving Logarithmic Growth

This article is devoted to exploring the properties on the logarithmic growth of entire functions represented by Laplace&ndash;Stieltjes transforms of zero order. In order to describe the growth of Laplace&ndash;Stieltjes transforms more finely, we introduce some concepts of the logarithmic indexes of the maximum term and the center index of the maximum term of Laplace&ndash;Stieltjes transforms, and establish some new inequalities focusing on the above logarithmic indexes, the logarithmic order, the (lower) logarithmic type and the coefficients of Laplace&ndash;Stieltjes transforms. Moreover, we obtain two estimation forms on the (lower) logarithmic type of entire functions represented by Laplace&ndash;Stieltjes transform by applying these inequalities. One estimation is mainly by the center indexes of the maximum term, the other is by the logarithmic order, exponent and coefficients. Finally, we obtain the equivalence condition of entire functions with the perfectly logarithmic linear growth. This result shows that the two estimation forms can be equivalent to some extent