Nearly Derivations on Banach Algebras

M. Eshaghi Gordji, H. Khodaei and G. H. Kim

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-8

Abstract:

Let 𠑛 be a fixed integer greater than 3 and let 𠜆 be a real number with 𠜆 ≠( 𠑛 2 − 𠑛 + 4 ) / 2 . We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖ ∑ 1 ≤ 𠑖 < 𠑗 ≤ 𠑛 1 ≤ 𠑘 𠑙 ≠𠑖 , 𠑗 ≤ 𠑛 𠑓 ( ( 𠑥 𠑖 + 𠑥 𠑗 ∑ ) / 2 + 𠑛 − 2 𠑙 = 1 𠑥 𠑘 𠑙 ∑ ) + 𠑓 ( 𠑛 𠑖 = 2 𠑥 𠑖 ) + 𠑓 ( 𠑥 1 ∑ ) ‖ ≤ ‖ 𠜆 𠑓 ( 𠑛 𠑖 = 1 𠑥 𠑖 ) ‖ .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:864340

DOI: 10.1155/2012/864340

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