Stability Of $n-$Dimensional Quartic Functional Equation In Felbin’s Spaces: Direct and Fixed Point Methods

M. Arunkumar, a S. Karthikeyan b and S. Ramamoorthi c∗

Stability Of $n-$Dimensional Quartic Functional Equation In Felbin’s Spaces: Direct and Fixed Point Methods

Authors :

M. Arunkumar,^a S. Karthikeyan ^b and S. Ramamoorthi ^c∗

Author Address :

^aDepartment of Mathematics, Government Arts College, Tiruvannamalai, TamilNadu, India-606 603.
^b Department of Mathematics, R.M.K. Engineering College, Kavarapettai, TamilNadu, India-601 206.
^c Department of Mathematics, Arunai Engineering College, Tiruvannamalai, TamilNadu, India-606 604.

*Corresponding author

Abstract :

In this paper, the authors investigate the generalized Ulam-Hyers stability of $n-$ dimensional quartic functional equation
\begin{align*}
\sum_{i=1}^n f\left(\sum_{j=1}^n x_{ij}\right)=& 6 \sum_{1\leq i<j<k\leq n}f\left(x_i+x_j+x_k\right)-(6n-18) \sum_{1\leq i<j\leq n}f\left(x_i+x_j\right) \\
&+2 \sum_{1\leq i<j\leq n}f\left(x_i-x_j\right)+(n-8)
f\left(\sum_{i=1}^n x_i\right)+\left(\frac{3n^2-17n+22}{16}\right)\sum\limits_{i=1}^n f(2x_i)
\end{align*} where
\begin{align*}
x_{ij}=\left\{
\begin{array}{rll}
-x_j & if & i=j;\\
x_j & if & i\neq j;
\end{array}\right.
\end{align*}
in Felbin’s type spaces using direct and fixed point methods.

Keywords :

Quartic functional equation, generalized Ulam-Hyers stability, Felbin’s type spaces, fixed point.

DOI :

Article Info :

Received : April 12, 2016; Accepted : November 23, 2016.