On the generalized cocycle equation of Ebanks and Ng
type: Item
instance of: scholarly article
title: On the generalized cocycle equation of Ebanks and Ng
zbMATH Open document ID: 0839.39009
DOI: 10.1007/BF03323046
published in: Results in Mathematics
publication date: 1996-06-19T00:00:00Z
review text: It is proved that the solution \(F_j : M^2 \to \Gamma\), \(j = 1, \dots, 6\), (where \(M\) is an abelian monoid and \(\Gamma\) is a uniquely 3-divisible abelian group) of a single functional equation considered by \textit{B. R. Ebanks} and \textit{C. T. Ng} [Aequationes Math. 46, No. 1-2, 76-90 (1993; Zbl 0801.39008)] may be decomposed into a sum of some functions \(G\) and \(H\) (mapping \(M^2\) into \(\Gamma)\) satisfying one of the following equations: \(\Delta_{xyz} G = \Delta_{yzx} G\) and \(\Delta_{xyz} H + \Delta_{yzx} H + \Delta_{zxy} H = 0\), where \(\Delta_{abc} K : = K(a + b,c) - K(a,c) - K(b,c)\).
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 785168
zbMATH Keywords: generalized cocycle equation
zbMATH Keywords: decomposition of solutions
zbMATH Keywords: abelian monoid
zbMATH Keywords: abelian group
author: T. M. K. Davison
reviewed by: Bogdan A. Choczewski
MaRDI profile type: Publication
cites work: On generalized cocycle equations
full work available at URL: https://doi.org/10.1007/bf03323046
OpenAlex ID: W2004956542
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description: scientific article; zbMATH DE number 785168