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Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces. (English) Zbl 1280.39019
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.

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
Full Text: DOI
[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
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