A Fixed Point Approach to the Stability of a General Mixed AQCQ-Functional Equation in Non-Archimedean Normed Spaces

Tian Zhou Xu, John Michael Rassias and Wan Xin Xu

Discrete Dynamics in Nature and Society, 2010, vol. 2010, 1-24

Abstract:

Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equation 𠑓 ( 𠑥 + 𠑘 𠑦 ) + 𠑓 ( 𠑥 − 𠑘 𠑦 ) = 𠑘 2 𠑓 ( 𠑥 + 𠑦 ) + 𠑘 2 𠑓 ( 𠑥 − 𠑦 ) + 2 ( 1 − 𠑘 2 ) 𠑓 ( 𠑥 ) + ( ( 𠑘 4 − 𠑘 2 ) / 1 2 ) [ 𠑓 ( 2 𠑦 ) + 𠑓 ( − 2 𠑦 ) − 4 𠑓 ( 𠑦 ) − 4 𠑓 ( − 𠑦 ) ] for a fixed integer 𠑘 with 𠑘 ≠0 , ± 1 in non-Archimedean normed spaces.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:812545

DOI: 10.1155/2010/812545

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