Sentence examples for satisfied the functional from inspiring English sources

Since all assumptions of Theorem 2.1 are satisfied, the functional I λ admits a sequence {u m = (u1m,..., u nm )} ⊂ X of critical points such that lim m → ∞ ( u 1 m, …, u n m ) = + ∞, and we have the conclusion.

The function satisfies the functional equation (1.5) which is thus called a cubic functional equation.

Obviously, the function satisfies the functional equation (1.1), which is called a cubic functional equation.

The function satisfies the functional equation (1.5), which explains why it is called cubic functional equation.

It is easy to show that the function satisfies the functional equation (1.2).

It is easy to show that the function satisfies the functional equation (1.2), which is called a quartic functional equation.

It is easy to show that the function satisfies the functional equation (1.5), which is called a quartic functional equation (see also [19]).

By a simple computation, one can show that the functions and satisfy the functional equation (1.10).

The quadratic function satisfies the functional equation.

Next, we will show that the function A n satisfies the functional equation (1).

It is easy to show that the function f(x) = x4 satisfies the functional equation (1.3), which is called a quartic functional equation (see also [33]).