Sentence examples for mapping is quartic from inspiring English sources

Therefore, the mapping is quartic.

By Lemma 2.1, the mapping is quartic.

Since the mapping is quartic (see [54, Lemma ]), we get that the mapping is quartic.

Therefore, (3.75) implies that the mapping is quartic.

By Lemma 2.1 we get that the mapping is quartic.

Taking the limit as, we find that satisfies (1.8) for all Hence, the mapping is quartic.

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).

If an even mapping satisfies (1.3), then is quartic.

By [[44], Lemma 2.1], the mapping Q : X → Y is quartic.

Arunkumar et al. [13] proved that a mapping (f:X rightarrow Y) satisfies the functional equation begin{aligned} &f(2x+y+z)+f(2x+y-z +f(2x+y-z +f(-2x+y+z)+f(2y)+f(2z) &quad =8bigl[f(x+f -2x+y+z+f -2x+y+zx-z)bigr]+2bigl[f(y+z)+f(y-z)bigr]+32f(x) end{aligned} (1.1) if and only if the mapping (f:X rightarrow Y) is quartic.

Therefore, f is quartic.