Park, Choonkil; Gordji, Madjid Eshaghi; Ghaemi, Mohammad Bagher; Majani, Hamid Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces. (English) Zbl 1280.39019 J. Inequal. Appl. 2012, Paper No. 289, 12 p. (2012). Summary: Using the fixed point method, we investigate the Hyers-Ulam stability of a system of additive-cubic-quartic functional equations with constant coefficients in non-Archimedean 2-normed spaces. Also, we give an example to show that some results in the stability of functional equations in (Archimedean) normed spaces are not valid in non-Archimedean normed spaces. Cited in 3 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 39B72 Systems of functional equations and inequalities 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis 39B52 Functional equations for functions with more general domains and/or ranges Keywords:octic functional equation; Hyers-Ulam stability; non-Archimedean 2-normed space; fixed point method; system of additive-cubic-quartic functional equations PDF BibTeX XML Cite \textit{C. Park} et al., J. Inequal. Appl. 2012, Paper No. 289, 12 p. (2012; Zbl 1280.39019) Full Text: DOI References: [1] doi:10.1002/mana.19630260109 · Zbl 0117.16003 · doi:10.1002/mana.19630260109 [2] doi:10.1002/mana.19640280102 · Zbl 0142.39803 · doi:10.1002/mana.19640280102 [3] doi:10.1002/mana.19690420414 · Zbl 0191.41202 · doi:10.1002/mana.19690420414 [4] doi:10.1002/mana.19690420104 · Zbl 0185.20003 · doi:10.1002/mana.19690420104 [5] doi:10.3336/gm.39.2.11 · Zbl 1072.46012 · doi:10.3336/gm.39.2.11 [6] doi:10.1016/j.jmaa.2010.10.004 · Zbl 1213.39028 · doi:10.1016/j.jmaa.2010.10.004 [7] doi:10.2307/2320670 · Zbl 0486.46054 · doi:10.2307/2320670 [8] doi:10.1073/pnas.27.4.222 · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222 [9] doi:10.1090/S0002-9939-1978-0507327-1 · doi:10.1090/S0002-9939-1978-0507327-1 [10] doi:10.1006/jmaa.1994.1211 · Zbl 0818.46043 · doi:10.1006/jmaa.1994.1211 [11] doi:10.1016/S0022-247X(02)00415-8 · Zbl 1021.39014 · doi:10.1016/S0022-247X(02)00415-8 [12] doi:10.1016/j.jmaa.2004.12.062 · Zbl 1072.39024 · doi:10.1016/j.jmaa.2004.12.062 [13] doi:10.1007/s00025-010-0018-4 · Zbl 1203.39016 · doi:10.1007/s00025-010-0018-4 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.