n-Expansively super-homogeneous and ( n , k ) $(n,k)$ -contractively sub-homogeneous fuzzy control functions and stability results with numerical examples

Abstract

Abstract We consider fuzzy sets and generalized triangular norms on positive elements of order commutative C ∗ $C^{*}$ -algebras to study the concept of C ∗ $C^{*}$ -algebra valued normed algebras with uncertainty. Using n-expansively super-homogeneous and ( n , k ) $(n,k)$ -contractively sub-homogeneous control functions, we make stochastic ( Θ , ϒ , Ξ ) $(\Theta,\Upsilon,\Xi )$ -derivations stable and get a better estimated error. We present some numerical examples of control functions and approximations to illustrate the applicability of the main results.

Keywords

• n-expansively super-homogeneous
• ( n , k ) $(n,k)$ -contractively sub-homogeneous
• Stochastic derivations
• Hyers–Ulam stability