Weighted sharing of three values and uniqueness of meromorphic functions
type: Item
instance of: scholarly article
title: Weighted sharing of three values and uniqueness of meromorphic functions
zbMATH Open document ID: 0996.30020
author: Indrajit Lahiri
published in: Kodai Mathematical Journal
publication date: 2002-05-15T00:00:00Z
review text: Let \(f\) and \(g\) be distinct nonconstant meromorphic functions in the complex plane, \(k\) a nonnegative integer or infinity, and \(a\) a member of \(\mathbb{C}\cup \{\infty\}\). Let \(E_k(a;f)\) be the set of all \(a\)-points of \(f\) where an \(a\)-point of multiplicity \(m\) is counted \(m\) times if \(m\leq k\) and \(k+1\) times if \(m>k\). If \(E_k(a;f)= E_k(a;g)\), then \(f\) and \(g\) are said to share the value \(a\) with weight \(k\). Using weighted sharing the author proves results on the uniqueness of meromorphic functions sharing three values in the complex plane which improve theorems of \textit{H. Ueda} [Kodai Math. J. 3, 457-471 (1980; Zbl 0468.30023)], \textit{H. X. Yi} [Chin. Ann. Math., Ser. A 9, 434-439 (1988; Zbl 0699.30024)], and \textit{S. Z. Ye} [Kodai Math. J. 15, 236-243 (1992; Zbl 0767.30026)].
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1742086
reviewed by: Linda R. Sons
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1106168813
OpenAlex ID: W2007977297
DOI: 10.2996/KMJ/1106168813
description: scientific article; zbMATH DE number 1742086