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Zbl 1187.46067
Mirmostafaee, Alireza Kamel
A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces. (English)
[J] Fuzzy Sets Syst. 160, No. 11, 1653-1662 (2009). ISSN 0165-0114

Summary: We define a notion for a quasi fuzzy $p$-normed space, then we use the fixed point alternative theorem to establish Hyers-Ulam-Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy $p$-normed space. Later, we show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, control function and the unique quartic mapping which approximates the almost quartic map. Finally, some applications of our results in the stability of quartic mappings from a linear space into a quasi $p$-norm space will be exhibited.

MSC 2000:: *46S40 Fuzzy functional analysis
39B82 Stability, separation, extension, and related topics

Keywords: fuzzy normed space; quartic functional equation; fixed point alternative; Hyers-Ulam-rassias stability; fuzzy stability

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