Abstract
Abstract Let n = 3 k + 2 for some k ∈ N . We investigate the generalized Hyers-Ulam stability of n-homomorphisms and n-derivations on fuzzy ternary Banach algebras related to the generalized Cauchy-Jensen additive functional equation. MSC:39B52, 46S40, 26E50.
Highlights
We say a functional equation (ξ ) is stable if any function g satisfying the equation (ξ ) approximately is near to a true solution of (ξ )
We say that a functional equation (ξ ) is superstable if every approximately solution of (ξ ) is an exact solution of it
Let f : E –→ E be a mapping between Banach spaces such that f (x + y) – f (x) – f (y) ≤ δ for all x, y ∈ E and for some δ >
Summary
We say a functional equation (ξ ) is stable if any function g satisfying the equation (ξ ) approximately is near to a true solution of (ξ ). Let f : E –→ E be a mapping between Banach spaces such that f (x + y) – f (x) – f (y) ≤ δ for all x, y ∈ E and for some δ > . There exists a unique additive mapping T : E –→ E such that f (x) – T(x) ≤ δ for all x ∈ E. (Th.M. Rassias) Let f : E → E be a mapping from a normed vector space E
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