scholarly journals A result on a question of Lü, Li and Yang

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2893-2906
Author(s):  
Sujoy Majumder ◽  
Somnath Saha
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Transcendental Meromorphic Function

Let f be a transcendental meromorphic function of finite order with finitely many poles, c ? C\{0} and n,k ? N. Suppose fn(z)-Q1(z) and (fn(z+c))(k)- Q2(z) share (0,1) and f(z), f(z+c) share 0 CM. If n ? k + 1, then (fn(z+c))(k) ? Q2(z)/Q1(z)fn(z), where Q1, Q2 are polynomials with Q1Q2 ?/ 0. Furthermore, if Q1 = Q2, then f(z)=c1e?/n z, where c1 and ? are non-zero constants such that e?c = 1 and ?k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

scholarly journals A note on a result of Singh and Kulkarni

2000 ◽  
Vol 23 (4) ◽  
pp. 285-288 ◽  
Author(s):  
Mingliang Fang
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Transcendental Meromorphic Function

We prove that iffis a transcendental meromorphic function of finite order and∑a≠∞δ(a,f)+δ(∞,f)=2, thenK(f(k))=2k(1−δ(∞,f))1+k−kδ(∞,f), whereK(f(k))=limr→∞N(r,1/f(k))+N(r,f(k))T(r,f(k))This result improves a result by Singh and Kulkarni.

scholarly journals On the common right factors of meromorphic functions

1997 ◽  
Vol 55 (3) ◽  
pp. 395-403 ◽  
Author(s):  
Tuen-Wai Ng ◽  
Chung-Chun Yang
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Rational Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Transcendental Meromorphic Function ◽  
The Common ◽  
Periodic Entire Function

In this paper, common right factors (in the sense of composition) of p1 + p2F and p3 + p4F are investigated. Here, F is a transcendental meromorphic function and pi's are non-zero polynomials. Moreover, we also prove that the quotient (p1 + p2F)/(p3 + p4F) is pseudo-prime under some restrictions on F and the pi's. As an application of our results, we have proved that R (z) H (z)is pseudo-prime for any nonconstant rational function R (z) and finite order periodic entire function H (z).

scholarly journals Uniqueness of difference polynomials

2021 ◽  
Vol 6 (10) ◽  
pp. 10485-10494
Author(s):  
Xiaomei Zhang ◽  
◽  
Xiang Chen ◽  
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Complex Numbers ◽  
Nonzero Constant ◽  
Transcendental Meromorphic Function ◽  
Difference Polynomial ◽  
Difference Polynomials

<abstract><p>Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)c)+\cdots+a_{1}f(z+c)+a_{0}f(z) $, where $ a_{k} (k = 0, 1, 2, \cdots, n) $ are not all zero complex numbers. In this paper, the authors investigate the uniqueness problems of $ P(z, f) $.</p></abstract>

scholarly journals Fixed points of differences of meromorphic functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zhaojun Wu ◽  
Jia Wu
Keyword(s):  
Meromorphic Function ◽  
Fixed Points ◽  
Finite Order ◽  
Complex Number ◽  
Meromorphic Functions ◽  
Acta Math ◽  
Transcendental Meromorphic Function ◽  
Nonzero Complex Number ◽  
Discrete Analogues

Abstract Let f be a transcendental meromorphic function of finite order and c be a nonzero complex number. Define $\Delta _{c}f=f(z+c)-f(z)$ Δ c f = f ( z + c ) − f ( z ) . The authors investigate the existence on the fixed points of $\Delta _{c}f$ Δ c f . The results obtained in this paper may be viewed as discrete analogues on the existing theorem on the fixed points of $f'$ f ′ . The existing theorem on the fixed points of $\Delta _{c}f$ Δ c f generalizes the relevant results obtained by (Chen in Ann. Pol. Math. 109(2):153–163, 2013; Zhang and Chen in Acta Math. Sin. New Ser. 32(10):1189–1202, 2016; Cui and Yang in Acta Math. Sci. 33B(3):773–780, 2013) et al.

scholarly journals On Properties of Differences Polynomials about Meromorphic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Jianming Qi ◽  
Jie Ding ◽  
Wenjun Yuan
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Special Class ◽  
Meromorphic Functions ◽  
Value Distribution ◽  
Class Difference ◽  
Difference Polynomial

We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).

scholarly journals Value distribution of meromorphic functions concerning rational functions and differences

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mingliang Fang ◽  
Degui Yang ◽  
Dan Liu
Keyword(s):  
Positive Integer ◽  
Meromorphic Function ◽  
Rational Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Rational Functions ◽  
Value Distribution ◽  
Exponent Of Convergence ◽  
Nonzero Constant ◽  
Zero Points

AbstractLet c be a nonzero constant and n a positive integer, let f be a transcendental meromorphic function of finite order, and let R be a nonconstant rational function. Under some conditions, we study the relationships between the exponent of convergence of zero points of $f-R$ f − R , its shift $f(z+nc)$ f ( z + n c ) and the differences $\Delta _{c}^{n} f$ Δ c n f .

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.

Power of meromorphic function sharing polynomials with derivative of it’s combination with it’s shift

2019 ◽  
Vol 69 (5) ◽  
pp. 1037-1052
Author(s):  
Sujoy Majumder ◽  
Somnath Saha
Keyword(s):  
Meromorphic Function ◽  
Transcendental Meromorphic Function ◽  
Function Sharing

Abstract In this paper we consider the situation when a power of a transcendental meromorphic function shares non-zero polynomials with derivative of it’s combination with it’s shift. Also we exhibit some examples to fortify the conditions of our results.

scholarly journals Value distribution of certain monomials of algebroid functions

1997 ◽  
Vol 62 (3) ◽  
pp. 398-404
Author(s):  
Kari Katajamäki
Keyword(s):  
Meromorphic Function ◽  
Value Distribution ◽  
Algebroid Function ◽  
Transcendental Meromorphic Function ◽  
Algebroid Functions

AbstractHayman has shown that if f is a transcendental meromorphic function and n ≽ 3, then fn f′ assumes all finite values except possibly zero infinitely often. We extend his result in three directions by considering an algebroid function ω, its monomial ωn0 ω′n1, and by estimating the growth of the number of α-points of the monomial.

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