Meromorphic functions that partially share values with their first derivative

Abstract

We consider uniqueness results for meromorphic functions $f:\mathbb{C}\to \hat{\mathbb{C}}$ such that for certain values $a\in \mathbb{C}$ the implication $f(z)=a\Rightarrow f^{\prime }(z)=a$ holds, i.e. that $f$ and $f^{\prime }$ share values {\it partially}. In particular, we give a result for four partially shared values.

12 pages