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ON CONTINUOUS SOLUTIONS OF AN EQUATION OF THE GOŁA̧B–SCHINZEL TYPE

Part of: Real functions

Published online by Cambridge University Press:  15 May 2012

ELIZA JABŁOŃSKA
ELIZA JABŁOŃSKA*
Affiliation:
Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 12, 35-959 Rzeszów, Poland (email: elizapie@prz.edu.pl)
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Abstract

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We characterise solutions f,g:ℝ→ℝ of the functional equation f(x+g(x)y)=f(x)f(y) under the assumption that f is continuous. Our considerations refer mainly to a paper by Chudziak [‘Semigroup-valued solutions of the Goła̧b–Schinzel functional equation’, Abh. Math. Semin. Univ. Hambg. 76, (2006), 91–98], in which the author studied the same equation assuming that g is continuous.

Keywords

generalised Goła̧b–Schinzel equation

MSC classification

Secondary: 26A03: Foundations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 10 - 17
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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