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A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces. (English) Zbl 1187.46067
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:
 46S40 Fuzzy functional analysis 39B82 Stability, separation, extension, and related topics