About this Journal Submit a Manuscript Table of Contents
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.

Linked References

  1. C. Alsina and J. L. Garcia Roig, “On a conditional cauchy equation on rhombuses,” in Functional Analysis, Approximation Theory and Numerical Analysis, pp. 5–7, World Scientific Publishing Company, River Edge, NJ, USA, 1994. View at Zentralblatt MATH · View at MathSciNet
  2. S. Gudder and D. Strawther, “Orthogonally additive and orthogonally increasing functions on vector spaces,” Pacific Journal of Mathematics, vol. 58, no. 2, pp. 427–436, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Rätz, “On orthogonally additive mappings,” Aequationes Mathematicae, vol. 28, no. 1-2, pp. 35–49, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Gy. Szabó, “ϕ-orthogonally additive mappings I,” Acta Mathematica Hungarica, vol. 58, no. 1-2, pp. 101–111, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Paganoni and J. Rätz, “Conditional functional equations and orthogonal additivity,” Aequationes Mathematicae, vol. 50, no. 1-2, pp. 135–142, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Gy. Szabó, “A conditional cauchy equation on normed spaces,” Publicationes Mathematicae Debrecen, vol. 42, no. 3-4, pp. 265–271, 1993. View at Zentralblatt MATH · View at MathSciNet
  7. R. C. James, “Orthogonality in normed linear spaces,” Duke Mathematical Journal, vol. 12, pp. 291–302, 1945. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Gy. Szabó, “Isosceles orthogonally additive mappings and inner product spaces,” Publicationes Mathematicae Debrecen, vol. 46, no. 3-4, pp. 373–384, 1995. View at Zentralblatt MATH · View at MathSciNet