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Shared values for differences and Borel exceptional values

  • Chuang-Xin Chen EMAIL logo and Zong-Xuan Chen
Published/Copyright: March 1, 2014
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Abstract.

In this paper, we prove that if f is a transcendental meromorphic function of finite order which has two Borel exceptional values a () and b ({}), and if f(z+η)-f(z) and f(z) share values d (d and da), b CM, f(z) is not periodic of period η (), then b=, da2,0 and f(z)=a+cec1z, where c,c1 are two nonzero constants.

MSC: 39A10; 30D35

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11171119, 11226090

Funding source: Natural Science Foundation of Guangdong Province, China

Award Identifier / Grant number: S2013040014347

The authors are grateful to the referee for a number of helpful suggestions to improve the paper.

Received: 2013-01-26
Revised: 2013-05-13
Accepted: 2013-10-09
Published Online: 2014-03-01
Published in Print: 2014-03-01

© 2014 by Walter de Gruyter Berlin/Boston

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