Abstract
Abstract Let P be a differential polynomial with constant coefficients and F a family of meromorphic functions in the unit disk. We study the situation that P[f] and P´[f] share a finite nonzero value CM for all f∈F and give conditions on P for F to be normal. Furthermore, a corresponding Picard type theorem for entire functions is given. Connections to Picard type theorems for exceptional values of differential polynomials are shown. The general results are applied to several specific differential polynomials such as P[u]:=u n +au (k) or P[u]:=u n u (k).
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