Value distribution of meromorphic functions and their differences
Let f(z) be a transcendental meromorphic function. Results are proved concerning the value distribution of the n'th forward difference Dnf(z), in terms of Borel exceptional values of f(z). The results may be partly viewed as discrete analogues of a classical theorem of Hayman dealing with the possible relationships between Picard exceptional values of f(z) and its derivatives.
Anahtar Kelimeler:
Complex difference; value distribution; Borel exceptional value
Value distribution of meromorphic functions and their differences
Let f(z) be a transcendental meromorphic function. Results are proved concerning the value distribution of the n'th forward difference Dnf(z), in terms of Borel exceptional values of f(z). The results may be partly viewed as discrete analogues of a classical theorem of Hayman dealing with the possible relationships between Picard exceptional values of f(z) and its derivatives.
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- Hinchliffe, J .D.: The Bergweiler—Eremenko theorem for finite lower order. Results Math. 43, 121—128 (2003).
- Weissenborn, G.: On the theorem of Tumura and Clunie. Bull. Lond. Math. Soc. 18, 371—373 (1986).
- Yang, C.C.: On deficiencies of differential polynomials, II. Math. Z. 125, 107—112 (1972).
- Ranran ZHANG, Zongxuan CHEN Received: 21.01.2011
- School of Mathematical Sciences,
- South China Normal University,
- Guangzhou 510631, People’s Republic of CHINA
- e—mails: zhrr19820315©163.c0m, chzx©vip.sina.com
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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