About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 240258, 5 pages
http://dx.doi.org/10.1155/2012/240258
Research Article

Approximate Riesz Algebra-Valued Derivations

Department of Mathematics, Faculty of Science, Çankırı Karatekin University, 18000 Çankırı, Turkey

Received 7 May 2012; Accepted 26 August 2012

Academic Editor: Janusz Brzdek

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 .