Normal Functions Concerning Shared Values (Communications in Mathematical Research, 2021)
In this paper we discuss normal functions concerning shared values. Weobtain 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 $f$ areof multiplicity, $f$ and $f′$ share $a$, then there exists a positive number $M$ such thatfor any $f ∈ \mathcal{F}, (1 − |z|^2) \frac{|f′(z)|}{1 + |f(z)|^2}  ≤ M$.