Shared values and normality

Abstract

This paper investigates the relationship between the normality and the shared values for a meromorphic function on the unit disc Δ. Based on Marty’s normality criterion and through a detailed analysis of the meromorphic functions, it is shown that if for every f ∈ $\mathcal{F}$$, f and f^(k) share a and b on Δ and the zeros of f(z) − a are of multiplicity k ⩾ 3, then $\mathcal{F}$$ is normal on Δ, where $\mathcal{F}$$ is a family of meromorphic functions on the unit disc Δ, and a and b are distinct values.

Keywords

meromorphic function / shared values / normal family / 30D35 / 30D45

References

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