Hyperstability of a Class of Linear Functional Equations
نویسندگان
چکیده
The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1 n n ∑ i=1 f(sφi(t)) (s, t ∈ S), where S is a semigroup and where φ1, . . . , φn : S → S are pairwise distinct automorphisms of S such that the set {φ1, . . . , φn} is a group equipped with the composition as the group operation. The main results state that if f satisfies a stability inequality related to the above equation then it is also a solution of this equation.
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