Stability of fuzzy orthogonally $*$-$n$-derivation in orthogonally fuzzy $C^*$-algebras

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Shiraz Branch‎, ‎Islamic Azad University‎, ‎Shiraz‎, ‎Iran

2 Department of Mathematics‎, ‎Semnan University P.O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran‎

10.22075/ijnaa.2021.4835

Abstract

‎In this paper‎, ‎using fixed point methods‎, ‎we prove the fuzzy orthogonally $*$-$n$-derivation on orthogonally fuzzy $C^*$-algebra for the functional equation‎
‎\begin{align*}‎
‎\begin{split}‎
‎f(\frac{\mu x+\mu y}{2}+\mu w)+f(\frac{\mu x+\mu w}{2}+\mu y)+f(\frac{\mu y+\mu w}{2}+\mu x)‎
‎=2\mu f(x)-2\mu f(y)-2\mu f(w)‎.
‎\end{split}‎
‎\end{align*}‎

Keywords