Stability Results of Additive-Quadratic \(n\)-Dimensional Functional Equation: Fixed Point Approach - Karthikeyan, S.; Rassias, J. M.; Vijayakumar, S.; Sakthivel, K. (Communications in Mathematics and Applications, 2022)
In this paper, the authors discussed the Ulam-Hyers stability results of \(n\)-dimensional mixed type additive and quadratic functional equation: \begin{align*} \sum\limits^{n}_{i=1}f\!\bigg(\sum\limits^{n}_{j=1}x_{ij}\bigg)\!& = \bigg(\frac{-n^2+7n-6}{2}\bigg)\!\! \sum_{i=1}^n f(x_i)+\!\bigg(\frac{-n^2+5n-2}{2}\bigg)\!\! \sum_{i=1}^n f(-x_i) \\ &\quad +\left(\frac{n-4}{2}\right) \sum_{1\le i<j\le n}(f(x_i+x_j) +f(-x_i-x_j))\,, \end{align*} where \begin{align*} x_{ij}= \begin{cases} -x_j&\text{if} \ i=j, \\ x_j &\text{if} \ i eq j, \end{cases} \end{align*} in Banach spaces using fixed point method.