Hyers-Ulam stability of a quadratic-additive functional equation in non-Archimedean fuzzy $\varphi$-2-normed spaces

Document Type : Research Paper


1 Department of Mathematics, Government Arts College for Men, Krishnagiri- 635 001, Tamil Nadu, India

2 Department of Data Science, Daejin University, Kyunggi 11159, Korea

3 Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, Korea



In this  work, we  introduce the following  quadratic-additive functional equation
&\psi\left(\sum_{a=1}^{n}  v_{a}\right)+\sum_{a=1}^{n}\psi\left(-v_{a}+\sum_{b=1;a\neq b}^{n} v_{b}\right)\nonumber \\= &\left(n-3\right) \sum_{1\leq a<b\leq n}\psi\left( v_{a}+  v_{b}\right)-\left(n^{2}-5n+2\right)\sum_{a=1}^{n} \left[ \frac{\psi(v_{a})+\phi(-v_{a})}{2}\right] -\left(n^{2}-5n+4\right)\sum_{a=1}^{n}  \left[\frac{\psi(v_{a})-\phi(-v_{a})}{2}\right]
where $n$ is a nonnegative integer in $\mathbb{N}-\{0,1,2\}$, and we prove the  Hyers-Ulam stability of the quadratic-additive functional equation in non-Archimedean fuzzy $\varphi$-2-normed space by utilizing two different techniques.


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Articles in Press, Corrected Proof
Available Online from 19 April 2024
  • Receive Date: 01 August 2022
  • Accept Date: 02 September 2022