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Every solution of the quartic functional equation is said to be a quartic mapping.
It is easy to show that the functionf(x) = x4 satisfies the functional equation (Equation 2), which is called aquartic functional equation, and every solution of the quartic functionalequation is said to be a quartic mapping.
It is easy to show that the function f(x) = x4 satisfies the functional equation (1), which is called a quartic functional equation and every solution of the quartic functional equation is said to be a quartic mapping.
It is easy to show that the function satisfies the functional equation (1.2), which is called a quartic functional equation and every solution of the quartic functional equation is said to be a quartic mapping.
It is easy to show that the function f ( x ) = x 4 satisfies functional equation (1.2), which is called a quartic functional equation, and every solution of the quartic functional equation is said to be a quartic mapping.
It is easy to show that the function f ( x ) = x 4 satisfies the functional equation (1.3), which is called a quartic functional equation, and every solution of the quartic functional equation is said to be a quartic mapping (for the stability of the ACQ and quartic functional equations, see [26, 31] and others).
Similar(54)
Thus is a quartic mapping.
Now, we show that Q is a quartic mapping.
So, we get (Q: X rightarrow Y) is a quartic mapping.
One can easily show that an even mapping satisfies (1.1) if and only if the even mapping is a quartic mapping, that is, (3.1).
(4 A mapping is called a -ternary quartic homomorphism briefly, -ternary 4-homomorphism if is a quartic mapping satisfying (2.1) for all.
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