Normal Criterion for Families of Meromorphic Functions and Shared Functions

This paper broadens the scope of existing research: the shared value is generalized from a non-zero finite complex number to a non-identically zero holomorphic function, the order of the derivative is extended from the first order to an arbitrary k-th order, and the constraint condition on the polynomial H is simplified to degH≥2. A more general normality criterion for families of meromorphic functions involving the sharing of differential polynomials is proved. Let D be a domain, F be a family of meromorphic functions in D, and P(z) be a non-identically zero holomorphic function in D. If for any f,g∈F, the differential polynomials H(f)f(k) and H(g)g(k) share P(z) in D, then F is normal in D.