Sentence examples for mapping a quadratic from inspiring English sources

Then there exist an additive mapping, a quadratic mapping, a cubic mapping and a quartic mapping such that (4.5).

Each mapping f : X → Y satisfying (1.4) can be realized as the sum of an additive mapping, a quadratic mapping, a cubic mapping and a quartic mapping.

In particular, a mapping (f : X to Y) is called an additive mapping, a quadratic mapping, a cubic mapping, a quadratic mapping, respectively, if f satisfies the functional equation (D_{1} f x,y) = 0), (D_{2} f x,y) = 0), (D_{3} f x,y) = 0), (D_{4} f x,y) = 0), respectively.

A mapping (f : V to W) is called a cubic-quadratic-additive mapping if and only if f is represented by the sum of an additive mapping, a quadratic mapping, and a cubic mapping.

A mapping (f : V to W) is called an additive mapping, a quadratic mapping, and a cubic mapping if f satisfies the functional equation (Af x,y) = 0), (Qf x,y) = 0), and (Cf x,y) = 0) for all (x, y in V), respectively.

One can easily show that an even mapping satisfies (1.1) if and only if the even mapping is a quadratic mapping, that is, (2.2).

It is shown that, if a mapping satisfies the following functional equation for all with, which is defined by the above equality, then the mapping is realized as the sum of an additive mapping and a quadratic mapping.

In 2002, Jung [24] obtained a stability of the functional equation (1.3) by taking and composing an additive map A and a quadratic map Q to prove the existence of a quadratic-additive mapping F, which is close to the given mapping f.

Then, there exist an additive mapping and a quadratic type mapping such that (2.49).

We call this quadratic mapping a generalized quadratic mapping of r-type.

Recall that a mapping is a quadratic multiplier if is a quadratic homogeneous mapping, and, for all (see [16]).