On the Stability of Quadratic Functional Equations

Jung Rye Lee, Jong Su An and Choonkil Park

Abstract and Applied Analysis, 2008, vol. 2008, 1-8

Abstract:

Let 𠑋 , 𠑌 be vector spaces and 𠑘 a fixed positive integer. It is shown that a mapping 𠑓 ( 𠑘 𠑥 + 𠑦 ) + 𠑓 ( 𠑘 𠑥 − 𠑦 ) = 2 𠑘 2 𠑓 ( 𠑥 ) + 2 𠑓 ( 𠑦 ) for all 𠑥 , 𠑦 ∈ 𠑋 if and only if the mapping 𠑓 ∶ 𠑋 → 𠑌 satisfies 𠑓 ( 𠑥 + 𠑦 ) + 𠑓 ( 𠑥 − 𠑦 ) = 2 𠑓 ( 𠑥 ) + 2 𠑓 ( 𠑦 ) for all 𠑥 , 𠑦 ∈ 𠑋 . Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:628178

DOI: 10.1155/2008/628178

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