FUZZY STABILITY OF THE M-DIMENSIONAL ADDITIVE FUNCTIONAL EQUATION

Abstract

In this article, we investigate the stability and hyperstability of the followingadditive functional equation:

f ( ∑_{i}^{m} ξ_i ) = ∑_{i}^{m} f(ξ_i)

within the framework of fuzzy normed vector spaces. Motivated by the concept of Hyers-Ulam stability and its generalizations, we adopt a xed point alternative method to analyzethe behavior of functions that approximately satisfy this equation. Using appropriate controlfunctions, we derive sucient conditions ensuring the existence and uniqueness of additivemappings that closely approximate the given function in a fuzzy sense. We also establishhyperstability results under natural asymptotic assumptions on the control functions. Theresults presented here extend and refine earlier stability studies of additive functional equa-tions, by embedding them in the context of fuzzy analysis and non-classical norm structures.Several corollaries are provided to demonstrate the applicability of our main theorems.