STABILITY OF MIXED TYPE ADDITIVE
QUADRATIC FUNCTIONAL EQUATION
IN RANDOM NORMED SPACE
S. Murthy1, M. Arunkumar2, G. Ganapathy3, P. Rajarethinam4
1Department of Mathematics
Government Arts College for Men
Krishnagiri, 635 001, Tamil Nadu, INDIA
2Department of Mathematics
Government Arts College
Tiruvannamalai, 606 603, Tamil Nadu, INDIA
3Department of Mathematics
R.M.D. Engineering College
Kavaraipettai, 601 206, Tamil Nadu, INDIA
4Department of Mathematics
Vysya College
Salem, 103, Tamil Nadu, INDIA
Abstract. In this paper, the authors obtain the general solution in vector space and generalized Ulam-Hyers stability of mixed type additive quadratic functional equation
\begin{align*} f(2x\pm y \pm z) = 2f(-x\mp y\mp z)-2f(\mp y \mp z)+f(\pm y \pm z)+3f(x)-f(-x) \end{align*}
in random normed space.
AMS Subject Classification: 39B52, 39B82
Key Words and Phrases: additive functional equation, quadratic functional equation, AQ-functional equation, Generalized Ulam-Hyers-Rassias stability, RN-space


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DOI: 10.12732/ijam.v26i2.3

Volume: 26
Issue: 2
Year: 2013