IJPAM: Volume 107, No. 2 (2016)

QUADRATIC FUNCTIONAL EQUATION ON
ORTHOGONALITY VECTOR SPACES

Sayed Khalil Ekrami$^1$, Madjid Mirzavaziri$^2$
$^1$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 $(X, \perp)$ be a real vector space of dimension at least 3, with the orthogonality defined on it by:


(i) for all $ x \in X $, $ x \perp 0 $ and $ 0 \perp x $,


(ii) for all $x, y \in X \setminus \lbrace 0 \rbrace$, $x \perp y$ if and only if $x, y$ are linearly independent.


We show that any orthogonally quadratic mapping on $ X $ 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

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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
Year: 2016
Volume: 107
Issue: 2
Pages: 381 - 391


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