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Keywords:
uniqueness; meromorphic function; differential polynomial; weighted sharing
uniqueness; meromorphic function; differential polynomial; weighted sharing
Summary:
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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