Abstract
In this paper, we establish the general solution of the functional equation ∑ i = 1 n f ( x i − 1 n ∑ j = 1 n x j ) = ∑ i = 1 n f ( x i ) − n f ( 1 n ∑ i = 1 n x i ) ( n ≥ 2 ) , and use a fixed point method to prove its generalized Hyers–Ulam stability in Banach modules over a unital Banach algebra.
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