Optimum Approximation for ζ-Lie Homomorphisms and Jordan ζ-Lie Homomorphisms in ζ-Lie Algebras by Aggregation Control Functions

In this work, by considering a class of matrix valued fuzzy controllers and using a (kappa,zeta)-Cauchy-Jensen additive functional equation ((kappa,zeta)-CJAFE), we apply the Radu-Mihet method (RMM), which is derived from an alternative fixed point theorem, and obtain the existence of a unique solution and the H-U-R stability (Hyers-Ulam-Rassias) for the homomorphisms and Jordan homomorphisms on Lie matrix valued fuzzy algebras with zeta members (zeta-LMVFA). With regards to each theorem, we consider the aggregation function as a matrix value fuzzy control function and investigate the results obtained.