Nearly Derivations on Banach Algebras. (5th April 2012)

• Record Type: Journal Article
• Authors: Gordji, M. Eshaghi; Khodaei, H.; Kim, G. H.
• Other Names: Rassias John Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-04-05
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/864340
• Languages: English
• ISSNs: 1026-0226

Abstract

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 ) ∥ .