Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (2): 380-386.doi: 10.1016/S0252-9602(14)60012-6

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AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

 WU Zhao-Jun   

  1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China
  • Received:2012-07-05 Online:2014-03-20 Published:2014-03-20
  • Supported by:

    The author is supported by the National Natural Science Foundation of China (11201395) and by the Science Foundation of Educational Commission of Hubei Province (Q20132801).

Abstract:

The author proves that if f : C→Cn is a transcendental vector valued mero-morphic function of finite order and assume ∑aCn∪{∞}δ(a) = 2, then,
1 − δ(∞)/2 − δ(∞)≤K(f′) ≤2(1 − δ(∞)/2 − δ(∞),
where
K(f ′) = limsup r→+∞N(r, f ′) + N (r, 0, f′)T(r, f ′).
This result extends the related results for meromorphic function by Singh and Kulkarni.

Key words: Characteristic function, vector valued meromorphic function, zero, pole

CLC Number: 

  • 30D35
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