Optimum Approximation for ς–Lie Homomorphisms and Jordan ς–Lie Homomorphisms in ς–Lie Algebras by Aggregation Control Functions

Abstract

In this work, by considering a class of matrix valued fuzzy controllers and using a (κ,ς)-Cauchy–Jensen additive functional equation ((κ,ς)-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 ς members (ς-LMVFA). With regards to each theorem, we consider the aggregation function as a matrix value fuzzy control function and investigate the results obtained.