📝 Abstract
Moslehian et al. investigated the fuzzy stability problems for the Cauchy additive functional equation and\nthe Jensen additive functional equation in fuzzy Banach spaces.\n\nUsing the fixed point method, we prove the Hyers-Ulam stability of the following quintic functional equations\n\\begin{eqnarray*}\n && f(3x+y) -5 f(2x+y) + f(2x-y) + 10f(x+y) - 5f(x-y) \\\\ && \\quad\n= 10 f(y) + f(3x) -3 f(2x) -27 f(x) , \\nonumber \\\\\n && f(3x+y) -5 f(2x+y) + f(2x-y) + 10f(x+y) - 5f(x-y) \\\\ && \\quad\n= 10 f(y) - 5f(3x) +42 f(2x) -9 f(x) \\nonumber\n \\end{eqnarray*} in fuzzy Banach spaces.\n\nWe prove that if every approximately quintic mapping from the set $\\mathbb N$ of positive integers into a fuzzy normed vector space can be approximated by a quintic mapping, then the fuzzy normed vector space is complete.
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