The Normality of Meromorphic Functions with Multiple Zeros and Poles Concerning Sharing Values

- Journal title : Kyungpook mathematical journal
- Volume 55, Issue 3, 2015, pp.641-652
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2015.55.3.641

Title & Authors

The Normality of Meromorphic Functions with Multiple Zeros and Poles Concerning Sharing Values

WANG, YOU-MING;

WANG, YOU-MING;

Abstract

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain and n, k be two positive integers such that , and let a, b be two finite complex constants such that . Suppose that (1) and share b in D for every pair of functions f, ; (2) All zeros of f have multiplicity at least k + 2 and all poles of f have multiplicity at least 2 for each in D; (3) Zeros of are not the b points of f(z) for each in D. Then F is normal in D. And some examples are provided to show the result is sharp.

Keywords

meromorphic functions;shared value;normal family;

Language

English

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