Meromorphic Functions Sharing a Nonzero Value with their Derivatives

- Journal title : Kyungpook mathematical journal
- Volume 55, Issue 1, 2015, pp.137-147
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2015.55.1.137

Title & Authors

Meromorphic Functions Sharing a Nonzero Value with their Derivatives

Li, Xiao-Min; Ullah, Rahman; Piao, Da-Xiong; Yi, Hong-Xun;

Li, Xiao-Min; Ullah, Rahman; Piao, Da-Xiong; Yi, Hong-Xun;

Abstract

Let f be a transcendental meromorphic function of finite order in the plane such that has finitely many zeros for some positive integer . Suppose that and f share a CM, where is a positive integer, is a finite complex value. Then f is an entire function such that , where is a nonzero constant. The results in this paper are concerning a conjecture of Bruck [5]. An example is provided to show that the results in this paper, in a sense, are the best possible.

Keywords

Meromorphic functions;Order of growth;Shared values;Uniqueness theorems;

Language

English

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