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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 878543, 6 pages
http://dx.doi.org/10.1155/2013/878543
Research Article

Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces

Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, I-10123 Torino, Italy

Received 20 March 2013; Accepted 6 June 2013

Academic Editor: Pedro M. Lima

Copyright © 2013 Margherita Fochi and Gabriella Viola. 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 real normed space with dimension greater than 2 and let be a real functional defined on . Applying some ideas from the studies made on the conditional Cauchy functional equation on the restricted domain of the vectors of equal norm and the isosceles orthogonal vectors, the conditional quadratic equation and the D’Alembert one, namely, and , have been studied in this paper, in order to describe their solutions. Particular normed spaces are introduced for this aim.