On entire and meromorphic functions that share small functions with their derivatives. (English) Zbl 1021.30030

Yu, Kit-Wing

JIPAM, J. Inequal. Pure Appl. Math. 4, No. 1, Paper No. 21, 7 p. (2003).

It is proved that if \(f\) is a nonconstant entire function, \(f\) and \(f^{(k)}\) share the small function \(a(\not\equiv 0,\infty)\) CM and \(\delta(0,f)> \frac 34\), then \(f\equiv f^{(k)}\). Furthermore, there is a similar conclusion for some meromorphic functions. Finally, several questions are posed.

Reviewer: Sun Daochun (Guangzhou)

MSC:

30D35

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Keywords:

derivatives; entire functions; meromorphic functions; uniqueness theorem; sharing values; Nevanlinna theory; small functions