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

Abstract

AbstractWe 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 $(\Theta,\Upsilon,\Xi )$ ( Θ , ϒ , Ξ ) -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.