Normal Criterion Concerning Shared Values

We study normal criterion of meromorphic functions shared values, we obtain the following. Let F be a family of meromorphic functions in a domain D, such that function f is an element of F has zeros of multiplicity at least 2, there exists nonzero complex numbers b(f), c(f) depending on f satisfying (i) b(f)/c(f) is a constant; (ii) min{sigma(0, b(f) ), sigma(0,c(f)), sigma(b(f), c(f) ) >= m} for some m > 0; (iii) (1/c(f)(k-1)) (f(1))(k) (z) + f (z) not equal b(f)(k)/c(f)(k-1) or (1/c(f)(k-1)) (f(1))(k) (z) + f(z) = (b(f)(k)/c(f)(k-1) double right arrow f(z) = b(f), then F is normal. These results improve some earlier previous results.