Mathematica Bohemica, Vol. 141, No. 3, pp. 297-313, 2016
Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial
Pulak Sahoo
Received February 14, 2014. First published June 15, 2016.
Abstract: Let $k$ be a nonnegative integer or infinity. For $a\in\mathbb{C}\cup\{\infty\}$ 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 $m\leq k$ 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).
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Affiliations: Pulak Sahoo, Department of Mathematics, University of Kalyani, Kalyani, District Nadia, 741235 West Bengal, India, e-mail: sahoopulak@yahoo.com, sahoopulak1@gmail.com
