scholarly journals Unicity of Entire Functions concerning Shifts and Difference Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dan Liu ◽  
Degui Yang ◽  
Mingliang Fang
Keyword(s):  
Entire Functions ◽  
Difference Operators ◽  
Unicity Theorem ◽  
Small Functions

We prove a unicity theorem of entire functions that share two distinct small functions with their shifts. The corollary of the theorem confirms the conjecture posed by Li and Gao (2011).

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.

On Entire Functions That Share Two Small Functions with Their Derivative

2018 ◽  
Vol 45 (3) ◽  
pp. 591-609
Author(s):  
Pulak Sahoo ◽  
Samar Halder
Keyword(s):  
Entire Functions ◽  
Small Functions

Uniqueness of entire functions sharing four small functions

1997 ◽  
Vol 119 (4) ◽  
pp. 841-858 ◽  
Author(s):  
Bao Qin Li
Keyword(s):  
Entire Functions ◽  
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.

scholarly journals Difference Equations and Sharing Values Concerning Entire Functions and Their Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhiqiang Mao ◽  
Huifang Liu
Keyword(s):  
Difference Equations ◽  
Entire Functions ◽  
Value Distribution ◽  
Difference Operators ◽  
Sharing Values ◽  
Difference Analogue ◽  
The Difference ◽  
Brück Conjecture

The value distribution of solutions of certain difference equations is investigated. As its applications, we investigate the difference analogue of the Brück conjecture. We obtain some results on entire functions sharing a finite value with their difference operators. Examples are provided to show that our results are the best possible.

scholarly journals Uniqueness Problems about Entire Functions with Their Difference Operator Sharing Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Fan Niu ◽  
Jianming Qi ◽  
Zhiyong Zhou
Keyword(s):  
Finite Order ◽  
Difference Operator ◽  
Entire Functions ◽  
Difference Operators ◽  
Transcendental Entire Functions

In this paper, we study the uniqueness questions of finite order transcendental entire functions and their difference operators sharing a set consisting of two distinct entire functions of finite smaller order. Our results in this paper improve the corresponding results from Liu (2009) and Li (2012).

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.

Entire functions sharing some values with their difference operators

2014 ◽  
Vol 57 (10) ◽  
pp. 2143-2152 ◽  
Author(s):  
Jie Zhang ◽  
LiangWen Liao
Keyword(s):  
Entire Functions ◽  
Difference Operators
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