Stability of \(n\)-dimensional mixed type quadratic and cubic functional equation
Authors
S. Karthikeyan
- Department of Mathematics, R.M.K. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
M. Suresh
- Department of Mathematics, R.M.D. Engineering College, Kavaraipettai-601 206, Tamil Nadu , India.
G. Ganapathy
- Department of Mathematics, R.M.D. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
V. B. Priya
- Department of Mathematics, R.M.K. College of Engineering and Technology, Puduvoyal-601 206, Tamil Nadu, India.
A. J. Bala
- Department of Mathematics, R.M.D. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
Abstract
Using Hyers' direct method, we introduced and proved generalized Ulam-Hyers stability of n-dimensional mixed-type quadratic and cubic functional equation of the form
\begin{eqnarray}
\sum\limits^{n}_{i=1}f\left(\sum\limits^{n}_{j=1}x_{ij}\right)& =& \left(\frac{n-6}{2}\right)
\left(\sum_{i=1}^n f(x_i)+\sum_{i=1}^n f(-x_i)\right)+\left(\frac{n}{2}\right)
\sum_{1\leq i < j\leq n} f(x_i+x_j)\\
&\quad&+\left(\frac{n-8}{2}\right)
\sum_{1\le i<j\le n}f\left(-x_i-x_j\right)+\left(\frac{-n^2+4n}{8}\right)\sum_{i=1}^n f(2x_i)
+\left(\frac{-n^2+8n-8}{8}\right)\sum_{i=1}^n f(-2x_i) ,
\end{eqnarray}
where
\[
x_{ij}=\left\{
\begin{array}{ll}
-x_j,& \text{if } i=j, \\
x_j ,&\text{if } i\neq j ,\\
\end{array}
\right.
\]
in Banach space.
Share and Cite
ISRP Style
S. Karthikeyan, M. Suresh, G. Ganapathy, V. B. Priya, A. J. Bala, Stability of \(n\)-dimensional mixed type quadratic and cubic functional equation, Journal of Mathematics and Computer Science, 31 (2023), no. 2, 214--224
AMA Style
Karthikeyan S., Suresh M., Ganapathy G., Priya V. B., Bala A. J., Stability of \(n\)-dimensional mixed type quadratic and cubic functional equation. J Math Comput SCI-JM. (2023); 31(2):214--224
Chicago/Turabian Style
Karthikeyan, S., Suresh, M., Ganapathy, G., Priya, V. B., Bala, A. J.. "Stability of \(n\)-dimensional mixed type quadratic and cubic functional equation." Journal of Mathematics and Computer Science, 31, no. 2 (2023): 214--224
Keywords
- Ulam-Hyers stability
- quadratic functional equation
- cubic functional equation
- Banach space
MSC
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