General Cubic-Quartic Functional Equation

M. Eshaghi Gordji, M. Kamyar and Th. M. Rassias

Abstract and Applied Analysis, 2011, vol. 2011, 1-18

Abstract:

We obtain the general solution and the generalized Hyers-Ulam stability of the general cubic-quartic functional equation for fixed integers k with 𠑘 ≠0 , ± 1 : ð ‘“ ( ð ‘¥ + 𠑘 𠑦 ) + ð ‘“ ( ð ‘¥ − 𠑘 𠑦 ) = 𠑘 2 ( ð ‘“ ( ð ‘¥ + 𠑦 ) + ð ‘“ ( ð ‘¥ − 𠑦 ) ) + 2 ( 1 − 𠑘 2 ) ð ‘“ ( ð ‘¥ ) + ( ( 𠑘 4 − 𠑘 2 ) / 4 ) ( ð ‘“ ( 2 𠑦 ) − 8 ð ‘“ ( 𠑦 ) ) + î ‚ î ‚ ð ‘“ ( 2 ð ‘¥ ) − 1 6 ð ‘“ ( ð ‘¥ ) , where î ‚ ð ‘“ ( ð ‘¥ ) ∶ = ð ‘“ ( ð ‘¥ ) + ð ‘“ ( − ð ‘¥ ) .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:463164

DOI: 10.1155/2011/463164

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