scholarly journals Two Entire Functions Sharing One Small Function CM and Two Other Small Functions IM

2001 ◽  
Vol 263 (1) ◽  
pp. 153-164
Author(s):  
Yao Weihong
Keyword(s):  
Entire Functions ◽  
Small Function ◽  
Small Functions

scholarly journals Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomialsL(f)=d2f″+d1f′+d0fgenerated by solutions of the above equation, whered0(z),d1(z),andd2(z)are entire functions that are not all equal to zero.

Entire functions sharing sets of small functions with their difference operators or shifts

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
BaoQin Chen ◽  
ZongXuan Chen
Keyword(s):  
Entire Functions ◽  
Difference Operators ◽  
Small Functions

AbstractWe show some interesting results concerning entire functions sharing two sets of small functions CM with their difference operators or shifts.

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 Entire functions of restricted hyper-order sharing a set of two small functions IM with their linear c-shift operators

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abhijit Banerjee ◽  
Arpita Roy
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Shift Operator ◽  
Research Work ◽  
Original Research ◽  
Exponent Of Convergence ◽  
Content Type ◽  
Shift Operators ◽  
Small Functions ◽  
Hyper Order

PurposeThe paper aims to build the relationship between an entire function of restricted hyper-order with its linear c-shift operator.Design/methodology/approachStandard methodology for papers in difference and shift operators and value distribution theory have been used.FindingsThe relation between an entire function of restricted hyper-order with its linear c-shift operator was found under the periphery of sharing a set of two small functions IM (ignoring multiplicities) when exponent of convergence of zeros is strictly less than its order. This research work is an improvement and extension of two previous papers.Originality/valueThis is an original research work.

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