Quartic functional equations

By Sang han Lee, S. Im, I. Hwang. 2005

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STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONS (2008, background): “3) if and only if there exists a unique symmetric multi-additive function B : X ×X ×X ×X → Y such that f(x) = B(x, x, x, x) for all x (see [2, 4], [16-21], [26, 27]).”
Stability of a Functional Equation Deriving from Cubic and Quartic Functions (2008, background): “4) if and only if there exists a unique symmetric multi-additive function Q : X×X×X×X −→ Y such that f(x) = Q(x, x, x, x) for all x (see also [3,4], [12-15], [33]).”
Solution and Stability of the Multiquadratic Functional Equation (2013, background): “Since then, the stability problems have been widely studied and extensively developed by many authors for a number of functional equations; see, for example, [4–10] and the books [11–14].”
The Stability of the Quartic Functional Equation in Random Normed Spaces (2010, unknown): “The interested reader is referred to [29] and (for the stability of the quartic functional equation) to the papers [5, 8, 18 , 26].”
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,”