Uniqueness of entire functions concerning difference polynomials

Chao Meng

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 1, page 89-97
  • ISSN: 0862-7959

Abstract

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In this paper, we investigate the uniqueness problem of difference polynomials sharing a small function. With the notions of weakly weighted sharing and relaxed weighted sharing we prove the following: Let f ( z ) and g ( z ) be two transcendental entire functions of finite order, and α ( z ) a small function with respect to both f ( z ) and g ( z ) . Suppose that c is a non-zero complex constant and n ≥ 7 (or n ≥ 10 ) is an integer. If f n ( z ) ( f ( z ) - 1 ) f ( z + c ) and g n ( z ) ( g ( z ) - 1 ) g ( z + c ) share “ ( α ( z ) , 2 ) ” (or ( α ( z ) , 2 ) * ), then f ( z ) ≡ g ( z ) . Our results extend and generalize some well known previous results.

How to cite

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Meng, Chao. "Uniqueness of entire functions concerning difference polynomials." Mathematica Bohemica 139.1 (2014): 89-97. <http://eudml.org/doc/261089>.

@article{Meng2014,
abstract = {In this paper, we investigate the uniqueness problem of difference polynomials sharing a small function. With the notions of weakly weighted sharing and relaxed weighted sharing we prove the following: Let $f(z)$ and $g(z)$ be two transcendental entire functions of finite order, and $\alpha (z)$ a small function with respect to both $f(z)$ and $g(z)$. Suppose that $c$ is a non-zero complex constant and $n\ge 7$ (or $n\ge 10$) is an integer. If $f^\{n\}(z)(f(z)-1)f(z+c)$ and $g^\{n\}(z)(g(z)-1)g(z+c)$ share “$(\alpha (z),2)$” (or $(\alpha (z),2)^\{*\}$), then $f(z)\equiv g(z)$. Our results extend and generalize some well known previous results.},
author = {Meng, Chao},
journal = {Mathematica Bohemica},
keywords = {entire function; difference polynomial; uniqueness; entire function; difference polynomial; uniqueness},
language = {eng},
number = {1},
pages = {89-97},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniqueness of entire functions concerning difference polynomials},
url = {http://eudml.org/doc/261089},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Meng, Chao
TI - Uniqueness of entire functions concerning difference polynomials
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 1
SP - 89
EP - 97
AB - In this paper, we investigate the uniqueness problem of difference polynomials sharing a small function. With the notions of weakly weighted sharing and relaxed weighted sharing we prove the following: Let $f(z)$ and $g(z)$ be two transcendental entire functions of finite order, and $\alpha (z)$ a small function with respect to both $f(z)$ and $g(z)$. Suppose that $c$ is a non-zero complex constant and $n\ge 7$ (or $n\ge 10$) is an integer. If $f^{n}(z)(f(z)-1)f(z+c)$ and $g^{n}(z)(g(z)-1)g(z+c)$ share “$(\alpha (z),2)$” (or $(\alpha (z),2)^{*}$), then $f(z)\equiv g(z)$. Our results extend and generalize some well known previous results.
LA - eng
KW - entire function; difference polynomial; uniqueness; entire function; difference polynomial; uniqueness
UR - http://eudml.org/doc/261089
ER -

References

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