# On a composite functional equation fulfilled by modulus of an additive function

On a composite functional equation fulfilled by modulus of an additive function - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Aequationes mathematicae

, Volume 80, Issue 1–2, pp 155–172

First Online: 08 June 2010Received: 27 June 2009Revised: 23 January 2010

Abstract

We deal with the problem of determining general solutions \{f\colon\mathbb{R}\to\mathbb{R}}\ of the following composite functional equation introduced by Fechner:$$ffx-fy=fx+y+fx-y-fx-fy.$$Our result gives a partial answer to this problem under some assumptions upon \{f\mathbb{R}}\. We are applying a theorem of Simon and Volkmann concerning a certain characterization of modulus of an additive function. A new proof of their result is also presented.Mathematics Subject Classification 200039B12 This research has been supported by the scholarship from the UPGOW project co-financed by the European Social Fund.

Dedicated to Janos Aczel on the occasion of his birthday.

Autor: Tomasz Kochanek