Sentence examples for be normal if there from inspiring English sources

(3) a cone is said to be normal if there exists such that implies that.

(b) a cone is said to be normal if there exists a constant such that implies.  . a cone is said to be normal if there exists a constant such that implies.

Recall that P is said to be normal if there exists a constant (N>0) such that (thetaleq xleq y) implies (|x| leq N|y|).

It is said to be normal if there is a number K > 0 such that for all x, y ∈ E, θ ⪯ x ⪯ y implies ∥ x ∥ ≤ K ∥ y ∥.

A cone P is said to be normal if there exists a positive constant δ such that |x+y|geqdelta, quadforall x, yin P, |x|=1, |y|=1.

A cone (P subset E) is said to be normal if there exists a constant (M > 0) such that (theta le x le y) implies (Vert x Vert le MVert y Vert ).

The cone K is normal if there exists d > 0 such that for all x, y ∈ X with 0 ⪯ x ⪯ y then ∥ x ∥ ≤ d ∥ y ∥.

Recall that cone is said to be solid if the interior is nonempty, and we denote if. is normal if there exists a positive constant such that implies, is called the normal constant of.

A cone P of a Banach space E is normal if there is some positive number N such that (x, y in E) and (thetapreceq xpreceq y) implies that (Vert xVert leq NVert yVert ), and the minimal N is called a normal constant of P.

Then (1) (xpreceq y) if (y-xin K);   (2) (xprec y) if (xpreceq y) and (xneq y);   (3) (xll y) if (y-xin operatorname{int} K);   (4) we say that K is normal if there is (M>0) such that (theta preceq xpreceq yRightarrow|x|leq M|y|).  .

(xpreceq y) if (y-xin K); (xprec y) if (xpreceq y) and (xneq y); (xll y) if (y-xin operatorname{int} K); we say that K is normal if there is (M>0) such that (theta preceq xpreceq yRightarrow|x|leq M|y|).