Functional equations characterizing the tangent function over a convex polygon
type: Item
instance of: scholarly article
title: Functional equations characterizing the tangent function over a convex polygon
zbMATH Open document ID: 1310.39013
author: Charinthip Hengkrawit
author: Vichian Laohakosol
author: Kanet Ponpetch
published in: Aequationes Mathematicae
publication date: 2014-12-16T00:00:00Z
review text: The authors generalize a result of \textit{T. Davison} [``Report of meeting 40th international symposium on functional equations'', ibid. 65, No. 3, 292 (2003)] and \textit{W. Benz} [Aequationes Math. 68, No. 1--2, 117--120 (2004; Zbl 1055.39036)] characterizing the tangent function. The Davison-Benz theorem solves a conditional functional equation involving three variables which can be interpreted as the angles of a non-degenerate triangle. The authors generalize this result to the case of \(n(\geq 3)\) variables which can serve as the angles of a non-degenerate convex \(n\)-gon.
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 6380866
zbMATH Keywords: functional equation
zbMATH Keywords: tangent function
zbMATH Keywords: non-degenerate convex \(n\)-gon
reviewed by: Bruce Ebanks
MaRDI profile type: Publication
full work available at URL: s00010-013-0229-3
OpenAlex ID: W1986118098
cites work: The functional equation \(f(x) f(y) f(z)= f(x)+ f(y)+ f(z)\)
cites work: Functional Equations and Inequalities with Applications
cites work: Q3992445
DOI: 10.1007/S00010-013-0229-3
description: scientific article; zbMATH DE number 6380866