Sentence examples for there exits a constant from inspiring English sources

Since, then there exits a constant such that a.e.

For,, then there exits a constant independent of and such that (4.6).

Thus, there exits a constant such that for all and, is fixed.

Let e 2 ∑ k = n n + m − 1 u k = M. Thus, there exits a constant M > 0 such that d ( x n + m, p ) ≤ M d ( x n, p ). for all n, m ∈ N and p ∈ F ( T ).

Meanwhile, we show that for any (tin[0,T]), there exits a constant (gamma'_{1}in 0,gamma_{1})) such that each positive T-periodic solution of Eq. (1.3) satisfies xbigl t-sigma(t)bigr)>gamma'_{1}.

A is said to be Lipschitz if there exits a constant L > 0 such that ∥ A x − A y ∥ ≤ L ∥ x − y ∥ 2, ∀ x, y ∈ C. For such a case, A is also said to be L-Lipschitz.

Therefore, there exits a positive constant (237).

Recall that an operator A of C into E is said to be α-inverse strongly accretive iff there exits a real constant α > 0 such that 〈 A x − A y, J ( x − y ) 〉 ≥ α ∥ A x − A y ∥ 2 ∀ x, y ∈ C. Evidently, the definition of an inverse-strongly accretive operator is based on that of an inverse-strongly monotone operator.

Recall that B is said to be an α-inverse-strongly monotone iff there exits a positive constant α such that 〈 B x − B y, x − y 〉 ≥ α ∥ B x − B y ∥ 2, ∀ x, y ∈ C. The classical variational inequality is to find u ∈ C such that 〈 B u, v − u 〉 ≥ 0, ∀ v ∈ C. (1.1).

(2 For every there exits a positive constants such that (2.12).

and there exits a convex neighborhood of such that (5.26).