Copyright © 2012 Faruk Polat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a Riesz algebra with an extended norm such that is complete. Also, let be another extended norm in weaker than such that whenever (a) and in , then ; (b) and in , then . Let and be two nonnegative real numbers. Assume that a map satisfies and for all . In this paper, we prove that there exists a unique derivation such that , (). Moreover, for all .