In this paper we deal with the product of two or three Cauchy differences equaled to zero. We show that in the case of two Cauchy differences, the condition of absolute continuity and differentiability of the two functions involved implies that one of them must be linear, i.e., we have a trivial solution. In the case of the product of three Cauchy differences the situation changes drastically: there exists non trivial C∞ solutions, while in the case of real analytic functions we obtain that at least one of the functions involved must be linear. Some open problems are then presented.

Alternative Cauchy equation in three unknown functions / G.L. Forti. - In: AEQUATIONES MATHEMATICAE. - ISSN 0001-9054. - (2021). [Epub ahead of print] [10.1007/s00010-021-00795-w]

Alternative Cauchy equation in three unknown functions

G.L. Forti
2021

Abstract

In this paper we deal with the product of two or three Cauchy differences equaled to zero. We show that in the case of two Cauchy differences, the condition of absolute continuity and differentiability of the two functions involved implies that one of them must be linear, i.e., we have a trivial solution. In the case of the product of three Cauchy differences the situation changes drastically: there exists non trivial C∞ solutions, while in the case of real analytic functions we obtain that at least one of the functions involved must be linear. Some open problems are then presented.
Alternative Cauchy equation; Analytic solution; C; ∞; solution
Settore MAT/05 - Analisi Matematica
15-mar-2021
Article (author)
File in questo prodotto:
File Dimensione Formato  
Forti2021_Article_AlternativeCauchyEquationInThr.pdf

accesso aperto

Descrizione: Online first
Tipologia: Publisher's version/PDF
Dimensione 308.75 kB
Formato Adobe PDF
308.75 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/880524
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact