Shared values and normality |
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| Authors: | Wen-hua Zhang Xue-cheng Pang |
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| Institution: | (1) Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China;(2) Department of Mathematics, East China Normal University, Shanghai, 200062, China |
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| 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 ∈
, f and f
(k) share a and b on Δ and the zeros of f(z) − a are of multiplicity k ⩾ 3, then
is normal on Δ, where
is a family of meromorphic functions on the unit disc Δ, and a and b are distinct values.
Selected from Journal of East China Normal University (Natural Science), 2003, 4: 12–18. This work was supported by the National Natural Science Foundation of China under grant number 10271122
and by Shanghai City Foundation for selected academic research |
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| Keywords: | meromorphic function shared values normal family |
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