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Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces. (English) Zbl 1177.39034

Summary: We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equation
\[ f(x+2y)+f(x - 2y)=4(f(x+y)+f(x - y)) - 24f(y) - 6f(x)+3f(2y) \]
in quasi-Banach spaces.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46B99 Normed linear spaces and Banach spaces; Banach lattices
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