Normal Functions Concerning Shared Values

Abstract

In this paper we discuss normal functions concerning shared values. We obtain the following result. Let $\mathcal{F}$ be a family of meromorphic functions in the unit disc ∆, and $a$ be a nonzero finite complex number. If for any $f ∈\mathcal{F}$, the zeros of $f$ are of multiplicity, $f$ and $f′$ share $a$, then there exists a positive number $M$ such that for any $f ∈ \mathcal{F}, (1 − |z|^2 ) \frac{|f′(z)|}{1 + |f(z)|^2}  ≤ M$.