IJPAM: Volume 107, No. 2 (2016)
ORTHOGONALITY VECTOR SPACES
Department of Mathematics
Payame Noor University
P.O. Box 19395-3697, Tehran, IRAN
Department of Pure Mathematics
Ferdowsi University of Mashhad
P.O. Box 1159, Mashhad 91775, IRAN
Abstract. Let be a real vector space of dimension at least 3, with the orthogonality defined on it by:
(i) for all , and ,
(ii) for all , if and only if are linearly independent.
We show that any orthogonally quadratic mapping on is a quadratic mapping. Also we prove the Hyers-Ulam stability of orthogonally quadratic functional equation and the Hyers-Ulam stability of orthogonally pexiderized quadratic functional equation.
Received: December 3, 2015
AMS Subject Classification: 39B52, 39B55, 39B82
Key Words and Phrases: quadratic functional equation, orthogonality space, stability
Download paper from here.
DOI: 10.12732/ijpam.v107i2.8 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 381 - 391