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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.

KeywordsComposite functional equation additive function  Download to read the full article text



Autor: Tomasz Kochanek

Fuente: https://link.springer.com/







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