The generalized Hyers–Ulam–Rassias stability of a cubic functional equation☆

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Stability of a Functional Equation Deriving from Cubic and Quartic Functions (2008, unknown): “The oldest cubic functional equation, and was introduced by J. M. Rassias (in 2000-2001): [17-18], as follows: f(x+ 2y) + 3f(x) = 3f(x+ y) + f(x− y) + 6f(y).”
Elementary remarks on Ulam–Hyers stability of linear functional equations (2007, background): “Many of them treat functional equations in several variables and what is given is an inequality in several variables and the first step in order to prove stability consists in certain manipulations transforming that inequality in several variables in an inequality in one variable (see, for instance,”
Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces (2008, background): “) is a function such that Φ(x,y) := X∞ i=0 1 4i+1 ϕ(2ix,2iy) <∞ for all x,y∈ G.Then there exists a unique quadratic mapping Q: G→ Xwith the property kf(x) −Q(x)k ≤ Φ(x,x) for all x∈ G. Jun and Kim [13] introduced the following cubic functional equation f(2x+y) + f(2x− y) = 2f(x+ y)+ 2f(x− y)+ 12f”
Solution and stability of generalized mixed type cubic , quadratic and additive functional equation in quasi-Banach spaces (2008, background): “Jun and Kim [ 11 ] introduced the following cubic functional equation”