Skip to main content
Log in

Local Pexider and Cauchy equations

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript

Summary.

Without assuming regularity we answer the questions when from a connected open set \(D \subset {\mathbb{R}}^2\) there exist quasiextensions of the Cauchy equation

$$e(s + t) = e(s)e(t)\quad ((s, t) \in D)$$

and extensions of the Pexider equation

$$f(s + t) = g(s)h(t)\quad ((s, t) \in D)$$

to \({\mathbb{R}}^2\). Even when no (quasi) extensions exist, we determine the general solutions (both with and without regularity assumptions).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to János Aczél.

Additional information

Manuscript received: October 17, 2005 and, in final form, April 10, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aczél, J., Skof, F. Local Pexider and Cauchy equations. Aequ. math. 73, 311–320 (2007). https://doi.org/10.1007/s00010-006-2863-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-006-2863-5

Mathematics Subject Classification (2000).

Keywords.

Navigation