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Meromorphic Functions Sharing a Nonzero Value with their Derivatives

Xiao-Min Li|Hong-Xun Yi|Rahman ullah|Da-Xiong Piao
경북대학교 자연과학대학 수학과|2015.03|Kyungpook Mathematical Journal|제55권 제1호|pp. 137-147|DOI http://dx.doi.org/10.5666/KMJ.2015.55.1.137

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참고문헌

키워드

Meromorphic functionsShared valuesOrder of growthUniqueness theorems
주제분류수학

초록

Let f be a transcendental meromorphic function of finite order in theplane such that f(m) has finitely many zeros for some positive integer m≥2. Suppose that f(k) and f share a CM, where k≥1 is a positiveinteger, a≠0 is a finite complex value. Then f is an entire function such that f(k)-a=c(f-a), where c≠0 is a nonzero constant. The results in this paper are concerning a conjecture of Brück [5]. An example is provided to show that the results in this paper, in a sense, are the best possible.

Abstract

Let f be a transcendental meromorphic function of finite order in theplane such that f(m) has finitely many zeros for some positive integer m≥2. Suppose that f(k) and f share a CM, where k≥1 is a positiveinteger, a≠0 is a finite complex value. Then f is an entire function such that f(k)-a=c(f-a), where c≠0 is a nonzero constant. The results in this paper are concerning a conjecture of Brück [5]. An example is provided to show that the results in this paper, in a sense, are the best possible.

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