Solution and Ulam-Hyers Stability of A $r_i$ Type $n-$ Dimensional Additive Quadratic Functional Equation In Quasi Beta Normed Spaces

M. Arunkumara,* and P. Agilanb

Solution and Ulam-Hyers Stability of A $r_i$ Type $n-$ Dimensional Additive Quadratic Functional Equation In Quasi Beta Normed Spaces

Authors :

M. Arunkumar^a,* and P. Agilan^b

Author Address :

^aDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
^bDepartment of Mathematics, S.K.P. Engineering College, Tiruvannamalai - 606 611, TamilNadu, India.

*Corresponding author.

Abstract :

In this paper, the authors established the generalized Ulam- Hyers Stability of a $r_i$ type $n-$ dimensional Additive Quadratic functional equation
\begin{align*}
f\left(\sum\limits_{i=1}^{n}r_ix_i\right)=\sum\limits_{i=1}^{n}\left(\sum\limits_{j=1}^{2}\frac{r_i^j}{2}\left[f(x_i)+(-1)^jf(-x_i)\right]\right)
+\sum\limits_{1\leq i<j\leq n}\frac{r_ir_j}{4}\left(\sum\limits_{p=0}^{1}\left(\sum\limits_{q=0}^{1}(-1)^{p+q}f\left[(-1)^px_i+(-1)^qx_j\right]\right)\right)
\end{align*}
where $r_i$ and $n$ are positive integers with $n\geq2$ in quasi beta normed spaces.

Keywords :

Additive functional equations, Quadratic functional equation, Mixed type functional equation, Ulam - Hyers stability,

DOI :

Article Info :

Received : April 17, 2015; Accepted : May 23, 2015.