IJPAM: Volume 106, No. 1 (2016)

ORTHOGONAL STABILITY OF A MIXED TYPE
CUBIC-QUARTIC FUNCTIONAL EQUATION
IN NON-ARCHIMEDEAN SPACES

C. Gayathri$^1$, R. Arul$^2$
$^1$Department of Mathematics
Adhiyamaan College of Engineering
Dr. M.G.R. Nagar, Hosur, 635 109, Tamil Nadu, INDIA
$^2$Department of Mathematics
Kandaswami Kandar's College
P. Velur, 638 182, Namakkal, Tamil Nadu, INDIA


Abstract. Using direct method, we prove the Hyers-Ulam stability of the orthogonally cubic-quartic functional equation
\begin{align}
f(2x+y)+f(2x-y)=3f(x+y)+f(-x-y)+3f(x-y)+f(y-x)\n \\ +18f(x)+6f(-x)-3f(y)-3f(-y),\tag{1}
\end{align}
for all $x, y$ with $x \bot y$, in non-Archimedean Banach spaces. Here $\bot$ is the orthogonality in the sense of R$\ddot{a}$tz.

Received: August 28, 2015

AMS Subject Classification: 39B55, 47H10, 39B52, 46H25, 54E40, 12J25

Key Words and Phrases: Hyers-Ulam stability, orthogonally cubic-quartic functional equation, non-Archimedean Banach space, orthogonality space

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DOI: 10.12732/ijpam.v106i1.23 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: 106
Issue: 1
Pages: 291 - 300


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