IJPAM: Volume 113, No. 3 (2017)

Title

STABILITY OF AN ADDITIVE-QUARTIC
FUNCTIONAL EQUATION IN ORTHOGONALITY SPACES

Authors

S. Sekar$^1$, G. Mayelvaganan$^2$
$^{1}$Department of Mathematics
Government Arts College(Autonomous
Salem-636 007, Tamil Nadu, INDIA
$^{2}$Department of Mathematics
M.G.R College
Hosur-635 109, Tamil Nadu, INDIA

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quartic functional equation
\begin{align} f(x+2y)+f(x-2y)=f(2x+y)+f(2x-y)-f(2x)-7[f(x)+f(-x)]\n \\ +15[f(y)+f(-y)] , \quad \forall x, y \text{~~with~~} x\bot y, \end{align}
in orthogonality spaces. Here $\bot$ is the orthogonality in the sense of R$\ddot{a}$tz.

History

Received: December 19, 2016
Revised: January 23, 2017
Published: March 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 39B55, 47H10, 39B52, 46H25.
Key Words and Phrases: Hyers-Ulam stability; orthogonally additive-quaric functional equation;
orthogonality space; fixed point method.

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How to Cite?

DOI: 10.12732/ijpam.v113i3.9 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: 2017
Volume: 113
Issue: 3
Pages: 471 - 482


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