scholarly journals Value distribution of higher order differential-difference polynomial of an entire function

2019 ◽  
Vol 1 (7) ◽  
pp. 48-56
Author(s):  
Renukadevi Dyavanal ◽  
Jyoti Muttagi
Keyword(s):  
Entire Function ◽  
Higher Order ◽  
Value Distribution ◽  
Difference Polynomial

scholarly journals Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Theirq-Shift

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Haiwa Guan ◽  
Gang Wang ◽  
Qiuqin Luo
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Zero Order ◽  
Value Distribution ◽  
Nonzero Constant ◽  
Uniqueness Results ◽  
Difference Polynomial

We investigate value distribution and uniqueness problems of meromorphic functions with theirq-shift. We obtain that iffis a transcendental meromorphic (or entire) function of zero order, andQ(z)is a polynomial, thenafn(qz)+f(z)−Q(z)has infinitely many zeros, whereq∈ℂ∖{0},ais nonzero constant, andn≥5(orn≥3). We also obtain that zero-order meromorphic function share is three distinct values IM with itsq-difference polynomialP(f), and iflimsup r→∞(N(r,f)/T(r,f))<1, thenf≡P(f).

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 Entire functions that share a small function with their linear difference polynomial

2021 ◽  
Vol 7 (3) ◽  
pp. 3731-3744
Author(s):  
Minghui Zhange ◽  
◽  
Jianbin Xiao ◽  
Mingliang Fang
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Small Function ◽  
Difference Polynomial ◽  
Function Sharing

<abstract><p>In this paper, we investigate the uniqueness of an entire function sharing a small function with its linear difference polynomial. Our results improve some results due to Li and Yi <sup>[<xref ref-type="bibr" rid="b11">11</xref>]</sup>, Zhang, Chen and Huang <sup>[<xref ref-type="bibr" rid="b17">17</xref>]</sup>, Zhang, Kang and Liao <sup>[<xref ref-type="bibr" rid="b18">18</xref>,<xref ref-type="bibr" rid="b19">19</xref>]</sup> etc.</p></abstract>

scholarly journals On the value distribution of iterated entire functions

1999 ◽  
Vol 66 (1) ◽  
pp. 18-31 ◽  
Author(s):  
Zheng Jian-Hua
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Periodic Points ◽  
Value Distribution ◽  
Transcendental Entire Function

AbstractLet f be a transcendental entire function and denote the n-th iterate fn. For n ≥ 2, we give an explict estimate of the number of periodic points of f with period n, that is, fix-points of fn which are not fix-points of fk for 1 ≤ k <n.

On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain

2018 ◽  
Vol 25 (2) ◽  
pp. 187-194 ◽  
Author(s):  
Grigor Barsegian ◽  
Wenjun Yuan
Keyword(s):  
Differential Equations ◽  
Bounded Domain ◽  
Meromorphic Functions ◽  
Upper Bounds ◽  
Higher Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Painleve Equations ◽  
Complex Differential Equations ◽  
Similar Solutions

Abstract The value distribution and, in particular, the numbers of a-points, have not been studied for meromorphic functions which are solutions of some complex differential equations in a given domain. Instead, the numbers of good a-points and Ahlfors islands, which play to a certain extend a role similar to that of the numbers of a-points, have been considered in some recent papers. In this paper, we consider meromorphic functions in a given domain, which are the solutions of some higher order equations and largely generalize the solutions of Painlevé equations 3–6. We give the upper bounds for the numbers of good a-points and Ahlfors islands of similar solutions.

scholarly journals Value Distribution of Meromorphic Solutions and Their Derivatives of Complex Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Abdallah El Farissi
Keyword(s):  
Differential Equations ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Value Distribution ◽  
Meromorphic Solutions ◽  
Small Functions ◽  
Complex Differential Equations ◽  
Linear Differential ◽  
The Relationship ◽  
Derivatives Of

We deal with the relationship between the small functions and the derivatives of solutions of higher-order linear differential equations f(k)+Ak-1f(k-1)+⋯+A0f=0,   k≥2, where Aj(z)  (j=0,1,…,k-1) are meromorphic functions. The theorems of this paper improve the previous results given by El Farissi, Belaïdi, Wang, Lu, Liu, and Zhang.

scholarly journals Value Distribution of Certain Type of Difference Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Nan Li ◽  
Lianzhong Yang
Keyword(s):  
Entire Function ◽  
Finite Order ◽  
Value Distribution ◽  
Transcendental Entire Function ◽  
Difference Polynomials

We investigate the value distribution of difference productf(z)n∑i=1k‍aif(z+ci), forn≥2andn=1, respectively, wheref(z)is a transcendental entire function of finite order andai,ciare constants satisfying∑i=1k‍aif(z+ci)≢0.

Value Distribution and Uniqueness of Certain Higher Order q-difference Polynomials

2021 ◽  
Vol 88 (1-2) ◽  
pp. 72
Author(s):  
Renukadevi S. Dyavanal ◽  
Jyoti B. Muttagi
Keyword(s):  
Nevanlinna Theory ◽  
Higher Order ◽  
Value Distribution ◽  
Difference Polynomials

In this paper, by using Nevanlinna theory we investigate cer- tain types of higher order q-di erence polynomials and prove the results on value distribution and uniqueness.

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