Sentence examples for be a cubic mapping from inspiring English sources

Every solution of the cubic functional equations is said to be a cubic mapping.

It is easy to show that the function f ( x ) = x 3 satisfies functional equation (1.1), which is called a cubic functional equation and every solution of the cubic functional equation is said to be a cubic mapping.

In [20], Jun and Kim considered the following cubic functional equation: (1.2). which is called a cubic functional equation and every solution of the cubic functional equation is said to be a cubic mapping.

It is easy to show that the function satisfies the functional (1.10), which is called a cubic functional equation and every solution of the cubic functional equation is said to be a cubic mapping.

It is easy to show that the function f(x) = x3 satisfies the functional equation (1.2), which is called a cubic functional equation and every solution of the cubic functional equation is said to be a cubic mapping.

It is easy to show that the function satisfies the functional equation (1.2), which is called a cubic functional equation and every solution of the cubic functional equation is said to be a cubic mapping.

Now, we show that C is a cubic mapping.

for all x ∈ X. Therefore C is a cubic mapping, which is unique.

By [32], Lemma 2.2], C X X → Y is a cubic mapping, as desired.

By [32], Lemma 2.2], C : Y → X is a cubic mapping, as desired.

The proof of Theorem 2.2 shows that T is a cubic mapping.