scholarly journals Transcendental Singularities for a Meromorphic Function with Logarithmic Derivative of Finite Lower Order

2018 ◽  
Vol 19 (1) ◽  
pp. 117-133 ◽  
Author(s):  
J. K. Langley
Keyword(s):  
Meromorphic Function ◽  
Lower Order ◽  
Logarithmic Derivative ◽  
Finite Lower Order

A Quantitative Estimate on Fixed-Points of Composite Meromorphic Functions

1995 ◽  
Vol 38 (4) ◽  
pp. 490-495 ◽  
Author(s):  
Jian-Hua Zheng
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Fixed Points ◽  
Lower Order ◽  
Quantitative Estimate ◽  
Meromorphic Functions ◽  
Transcendental Entire Function ◽  
Logarithmic Density ◽  
Image Position ◽  
Finite Lower Order

AbstractLet ƒ(z) be a transcendental meromorphic function of finite order, g(z) a transcendental entire function of finite lower order and let α(z) be a non-constant meromorphic function with T(r, α) = S(r,g). As an extension of the main result of [7], we prove thatwhere J has a positive lower logarithmic density.

scholarly journals Radial distributions of Julia sets of meromorphic functions

2006 ◽  
Vol 81 (3) ◽  
pp. 363-368 ◽  
Author(s):  
Ling Qiu ◽  
Shengjian Wu
Keyword(s):  
Meromorphic Function ◽  
Lower Order ◽  
Meromorphic Functions ◽  
Julia Set ◽  
Julia Sets ◽  
Deficient Value ◽  
Borel Exceptional Value ◽  
Exceptional Value ◽  
Finite Lower Order

AbstractWe consider a meromorphic function of finite lower order that has ∞ as its deficient value or as its Borel exceptional value. We prove that the set of limiting directions of its Julia set must have a definite range of measure.

scholarly journals Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane

2020 ◽  
Vol 54 (2) ◽  
pp. 172-187
Author(s):  
I.E. Chyzhykov ◽  
A.Z. Mokhon'ko
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Half Plane ◽  
Meromorphic Functions ◽  
Logarithmic Derivative ◽  
Sharp Estimates ◽  
Exceptional Sets ◽  
Upper Half Plane ◽  
Logarithmic Derivatives

We established new sharp estimates outside exceptional sets for of the logarithmic derivatives $\frac{d^ {k} \log f(z)}{dz^k}$ and its generalization $\frac{f^{(k)}(z)}{f^{(j)}(z)}$, where $f$ is a meromorphic function $f$ in the upper half-plane, $k>j\ge0$ are integers. These estimates improve known estimates due to the second author in the class of meromorphic functions of finite order.Examples show that size of exceptional sets are best possible in some sense.

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