# Meromorphic function sharing a small function with a linear differential polynomial

Mathematica Bohemica (2016)

- Volume: 141, Issue: 1, page 1-11
- ISSN: 0862-7959

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topLahiri, Indrajit, and Sarkar, Amit. "Meromorphic function sharing a small function with a linear differential polynomial." Mathematica Bohemica 141.1 (2016): 1-11. <http://eudml.org/doc/276800>.

@article{Lahiri2016,

abstract = {The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and prove the following result: Let $f$ be a nonconstant meromorphic function and $L$ a nonconstant linear differential polynomial generated by $f$. Suppose that $a = a(z)$ ($\lnot \equiv 0, \infty $) is a small function of $f$. If $f-a$ and $L-a$ share $0$ CM and \[ (k+1)\overline\{N\}(r, \infty ; f)+ \overline\{N\}(r, 0; f^\{\prime \})+ N\_\{k\}(r, 0; f^\{\prime \})< \lambda T(r, f^\{\prime \})+ S(r, f^\{\prime \}) \]
for some real constant $\lambda \in (0, 1)$, then $ f-a=(1+ \{c\}/\{a\})(L-a)$, where $c$ is a constant and $1+\{c\}/\{a\} \lnot \equiv 0$.},

author = {Lahiri, Indrajit, Sarkar, Amit},

journal = {Mathematica Bohemica},

keywords = {meromorphic function; differential polynomial; small function; sharing},

language = {eng},

number = {1},

pages = {1-11},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Meromorphic function sharing a small function with a linear differential polynomial},

url = {http://eudml.org/doc/276800},

volume = {141},

year = {2016},

}

TY - JOUR

AU - Lahiri, Indrajit

AU - Sarkar, Amit

TI - Meromorphic function sharing a small function with a linear differential polynomial

JO - Mathematica Bohemica

PY - 2016

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 141

IS - 1

SP - 1

EP - 11

AB - The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and prove the following result: Let $f$ be a nonconstant meromorphic function and $L$ a nonconstant linear differential polynomial generated by $f$. Suppose that $a = a(z)$ ($\lnot \equiv 0, \infty $) is a small function of $f$. If $f-a$ and $L-a$ share $0$ CM and \[ (k+1)\overline{N}(r, \infty ; f)+ \overline{N}(r, 0; f^{\prime })+ N_{k}(r, 0; f^{\prime })< \lambda T(r, f^{\prime })+ S(r, f^{\prime }) \]
for some real constant $\lambda \in (0, 1)$, then $ f-a=(1+ {c}/{a})(L-a)$, where $c$ is a constant and $1+{c}/{a} \lnot \equiv 0$.

LA - eng

KW - meromorphic function; differential polynomial; small function; sharing

UR - http://eudml.org/doc/276800

ER -

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