Nearly Derivations on Banach Algebras. (5th April 2012) - Gordji, M. Eshaghi; Khodaei, H.; Kim, G. H.
Abstract : Letn be a fixed integer greater than 3 and letλ be a real number withλ ≠ ( n 2 - n + 4 ) / 2 . We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality∥ ∑ 1 ≤ i < j ≤ n 1 ≤ k l ≠ i, j ≤ n f ( ( x i + x j ) / 2 + ∑ l = 1 n - 2 x k l ) + f ( ∑ i = 2 n x i ) + f ( x 1 ) ∥ ≤ ∥ λ f ( ∑ i = 1 n x i ) ∥ .