Sentence examples for a satisfy from inspiring English sources

Assume that (T Arightarrow B) and (g: Arightarrow A) satisfy the following conditions: (a) T is a proximal contraction.

Assume that (T Arightarrow B) and (g Arightarrow A) satisfy the following conditions: (a) T is a proximal nonexpansive.

Assume that (T Arightarrow B) and (g Arightarrow A) satisfy the following conditions: (a) T is continuous affine proximal nonexpansive.

Let (S Arightarrow B) and (T Brightarrow A) satisfy the following conditions: (a) S and T are proximal contractions of the first kind.

Let (T Alongrightarrow B) and (g Alongrightarrow A) satisfy the following conditions: (a) T is a continuous proximal contraction of the first kind.

Let A and B be nonempty subsets of a metric space X, (A, B) and (B, A) satisfy the property UC*.

The eigenvalues (beta_{n}=frac{npi }{ b-a)}) satisfy the equation sin beta_{ b-a-a)=0,quad n=1,2,3,dots.

The relation of operators A and A ˜ satisfy that D ( A ) = { u ∈ H 0 1 , A ˜ u ∈ L 2 }, A u = A ˜ u for any  u ∈ D ( A ). From now on, both A and A ˜ are denoted simply by A. We introduce a simple example of the control operator B which satisfies the condition in Theorem 4.2.

To show that the matrices S [ j ], j ≥ 2, together with the matrix S [ 1 ] = ( A B C − A ∗ ), satisfy symplecticity condition (6) requires rather tedious computations.

The statements of two elements (tilde{A}_{p}) and (tilde{B}_{p}) in (mathcal {A}) satisfy that (tilde{A}_{p}) has a higher ranking than (tilde{B}_{p}) when (RM) is applied to the fuzzy numbers in (mathcal {A}) will be written as (tilde{A}_{p}succ tilde{B}_{p}) by (RM) on (mathcal {A}).

Let X be a nonempty set and let (d:Xtimes Xtomathbb{A}) satisfy (i) (d x,y succeq theta) for all (x,yin X) and (d x,y)=thetaiff x=y);   (ii) (d x,y)=d y,x)) for all (x,yin X);   (iii) (d x,y preceq d x,z +d z,y)) for all (x,y,zin X).