Generalized Hyers-Ulam Stability of Generalized ( ð ‘, ð ¾ ) -Derivations

M. Eshaghi Gordji, J. M. Rassias and N. Ghobadipour

Abstract and Applied Analysis, 2009, vol. 2009, 1-8

Abstract:

Let 3 ≤ ð ‘› , and 3 ≤ 𠑘 ≤ ð ‘› be positive integers. Let ð ´ be an algebra and let ð ‘‹ be an ð ´ -bimodule. A â„‚ -linear mapping ð ‘‘ ∶ ð ´ â†’ ð ‘‹ is called a generalized ( ð ‘› , 𠑘 ) -derivation if there exists a ( 𠑘 − 1 ) -derivation ð ›¿ ∶ ð ´ â†’ ð ‘‹ such that ð ‘‘ ( ð ‘Ž 1 ð ‘Ž 2 ⋯ ð ‘Ž ð ‘› ) = ð ›¿ ( ð ‘Ž 1 ) ð ‘Ž 2 ⋯ ð ‘Ž ð ‘› + ð ‘Ž 1 ð ›¿ ( ð ‘Ž 2 ) ð ‘Ž 3 ⋯ ð ‘Ž ð ‘› + ⋯ + ð ‘Ž 1 ð ‘Ž 2 ⋯ ð ‘Ž 𠑘 − 2 ð ›¿ ( ð ‘Ž 𠑘 − 1 ) ð ‘Ž 𠑘 ⋯ ð ‘Ž ð ‘› + ð ‘Ž 1 ð ‘Ž 2 ⋯ ð ‘Ž 𠑘 − 1 ð ‘‘ ( ð ‘Ž 𠑘 ) ð ‘Ž 𠑘 + 1 ⋯ ð ‘Ž ð ‘› + ð ‘Ž 1 ð ‘Ž 2 ⋯ ð ‘Ž 𠑘 ð ‘‘ ( ð ‘Ž 𠑘 + 1 ) ð ‘Ž 𠑘 + 2 ⋯ ð ‘Ž ð ‘› + ð ‘Ž 1 ð ‘Ž 2 ⋯ ð ‘Ž 𠑘 + 1 ð ‘‘ ( ð ‘Ž 𠑘 + 2 ) ð ‘Ž 𠑘 + 3 ⋯ ð ‘Ž ð ‘› + ⋯ + ð ‘Ž 1 ⋯ ð ‘Ž ð ‘› − 1 ð ‘‘ ( ð ‘Ž ð ‘› ) for all ð ‘Ž 1 , ð ‘Ž 2 , … , ð ‘Ž ð ‘› ∈ ð ´ . The main purpose of this paper is to prove the generalized Hyers-Ulam stability of the generalized ( ð ‘› , 𠑘 ) -derivations.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:437931

DOI: 10.1155/2009/437931

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