IJPAM: Volume 81, No. 1 (2012)

HYERS-ULAM-RASSIAS STABILITY OF ORTHOGONALLY
CUBIC AND QUARTIC FUNCTIONAL EQUATIONS

Ashish$^1$, Renu Chugh$^2$
$^{1,2}$Department of Mathematics
Maharshi Dayanand University
Rohtak, 124001, INDIA


Abstract. In this paper, the Hyers-Ulam-Rassias Stability of the following orthogonal Cubic and Quartic functional equations:
\begin{align} &f (x\! +\! 3y)\!-\!3f (x\! +\! y) + 3f (x\!-\!y)\!-\!f (x\!-\!3y... ...y) \nonumber\\ &\qquad= 64f (x) + 64f (y) + 24f (x + y)-6f (x-y), \end{align}
in the setting of orthogonality space is established, where $f $ is a mapping from an orthogonality space $(X,\perp)$ into a real Banach space $Y$.

Received: March 13, 2012

AMS Subject Classification: 39B55, 39B52, 39B82, 46H25

Key Words and Phrases: cubic functional equation, quartic functional equation, Hyers-Ulam-Rassias stability, orthogonality spaces

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 1