scholarly journals Uniqueness of entire function sharing a small function with its derivative

2010 ◽  
Vol 362 (2) ◽  
pp. 387-392 ◽  
Author(s):  
Jun Wang
Keyword(s):  
Entire Function ◽  
Small Function ◽  
Function Sharing

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>

Entire function sharing a small function with its mixed-operators

2019 ◽  
Vol 26 (1) ◽  
pp. 47-62 ◽  
Author(s):  
Xianjing Dong ◽  
Kai Liu
Keyword(s):  
Entire Function ◽  
Linear Combination ◽  
Small Function ◽  
Uniqueness Problem ◽  
Difference Operators ◽  
Transcendental Entire Function ◽  
Shift Operators ◽  
Function Sharing

Abstract In this article, we investigate the uniqueness problem on a transcendental entire function {f(z)} with its linear mixed-operators Tf, where T is a linear combination of differential-difference operators {D^{\nu}_{\eta}:=f^{(\nu)}(z+\eta)} and shift operators {E_{\zeta}:=f(z+\zeta\/)} , where {\eta,\nu,\zeta} are constants. We obtain that if a transcendental entire function {f(z)} satisfies {\lambda(f-\alpha)<\sigma(f\/)<+\infty} , where {\alpha(z)} is an entire function with {\sigma(\alpha)<1} , and if f and Tf share one small entire function {a(z)} with {\sigma(a)<\sigma(f\/)} , then {\frac{Tf-a(z)}{f(z)-a(z)}=\tau,} where τ is a non-zero constant. Furthermore, we obtain the value τ and the expression of f by imposing additional conditions.

AN ENTIRE FUNCTION SHARING TWO VALUES WITH ITS LINEAR DIFFERENTIAL POLYNOMIAL

2017 ◽  
Vol 97 (2) ◽  
pp. 265-273
Author(s):  
INDRAJIT LAHIRI
Keyword(s):  
Entire Function ◽  
Differential Polynomial ◽  
Value Sharing ◽  
Linear Differential Polynomial ◽  
Linear Differential ◽  
Function Sharing

We consider the uniqueness of an entire function and a linear differential polynomial generated by it. One of our results improves a result of Li and Yang [‘Value sharing of an entire function and its derivatives’, J. Math. Soc. Japan51(4) (1999), 781–799].

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