Sharing functions and normal families involving higher-order derivatives
Take positives integers m≥ 0,n≥ 2,k≥ 1.Let F be a family of meromorphic functions defined in a domain D.Let φ(z)≠ 0 be an analytic function with zeros of multiplicity m in a domain D.Let P be a polynomial with deg(P)≥ 3 and had at least one q-fold zero,m can be divisible by n+q.For every f ∈ F,f has only zeros with multiplicity at least k+m/q,and all its poles of multiplicity at least m+1.If P(f)(f(k))n and P(g)(g(k))n share φ(z)in D for each pair of(f,g)∈ F,then F is normal in D.
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