ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION

By J. Chung, Prasanna K. Sahoo. 2003

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Quadratic-Quartic Functional Equations in RN-Spaces (2009, background): “3), which is called a quartic functional equation (see also [6]).”
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]).”
STABILITY OF A FUNCTIONAL EQUATION DERIVING FROM QUARTIC AND ADDITIVE FUNCTIONS (2008, background): “ a function f between real vector spaces X and Y is a solution of (1.3) 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 [3,4], [12, 13, 14, 15, 16, 17], [22,23]). It is easy to show that the function f(x) = x4 satisﬁes t”