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Department of Mathematics,East China Normal University, Shanghai 20062,China 2.Department of Mathematics, East China University of Science and Technology,Shanghai 200237,China
Let ∮be a family of meromorphic function on the unit disc ⊿ and let a and b be distinct values. If for every f∈∮, f and f(k) share a and b on ⊿ and the zero of f(z)-a are of multiplicity ≧k,where k≧3 be a positive integer,then ∮ is normal on ⊿.