Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial

Pulak Sahoo

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 3, page 297-313
  • ISSN: 0862-7959

Abstract

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Let k be a nonnegative integer or infinity. For a ∈ ℂ ∪ { ∞ } we denote by E k ( a ; f ) the set of all a -points of f where an a -point of multiplicity m is counted m times if m ≤ k and k + 1 times if m > k . If E k ( a ; f ) = E k ( a ; g ) then we say that f and g share the value a with weight k . Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).

How to cite

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Sahoo, Pulak. "Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial." Mathematica Bohemica 141.3 (2016): 297-313. <http://eudml.org/doc/286848>.

@article{Sahoo2016,
abstract = {Let $k$ be a nonnegative integer or infinity. For $a\in \mathbb \{C\}\cup \lbrace \infty \rbrace $ we denote by $E_\{k\}(a;f)$ the set of all $a$-points of $f$ where an $a$-point of multiplicity $m$ is counted $m$ times if $m\le k$ and $k+1$ times if $m>k$. If $E_\{k\}(a;f)= E_\{k\}(a;g)$ then we say that $f$ and $g$ share the value $a$ with weight $k$. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).},
author = {Sahoo, Pulak},
journal = {Mathematica Bohemica},
keywords = {uniqueness; meromorphic function; differential polynomial; weighted sharing},
language = {eng},
number = {3},
pages = {297-313},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial},
url = {http://eudml.org/doc/286848},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Sahoo, Pulak
TI - Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 3
SP - 297
EP - 313
AB - Let $k$ be a nonnegative integer or infinity. For $a\in \mathbb {C}\cup \lbrace \infty \rbrace $ we denote by $E_{k}(a;f)$ the set of all $a$-points of $f$ where an $a$-point of multiplicity $m$ is counted $m$ times if $m\le k$ and $k+1$ times if $m>k$. If $E_{k}(a;f)= E_{k}(a;g)$ then we say that $f$ and $g$ share the value $a$ with weight $k$. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).
LA - eng
KW - uniqueness; meromorphic function; differential polynomial; weighted sharing
UR - http://eudml.org/doc/286848
ER -

References

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