Sentence examples for be an increasing operator from inspiring English sources

An operator (Phi: mathbb{C}rightarrowmathbb{E}) is said to be an increasing operator if begin{aligned} x, yinmathbb{C},quad xpreceq yquad Rightarrowquad Phi xpreceqPhi y. end{aligned} Similarly, An operator (Phi: mathbb{C}rightarrowmathbb{E}) is called a decreasing operator if begin{aligned} x, yinmathbb{C},quad xpreceq yquad Rightarrowquad Phi xsucceqPhi y. end{aligned}.

Let P be a normal cone in E, and (T Prightarrow P) be an increasing operator.

Theorem 2.1 Let P be a normal cone, A : P → P be an increasing operator and B : P → P be a decreasing operator.

Theorem 2.7 Let P be a normal cone, A : P → P be an increasing operator and B : P × P → P be a mixed monotone operator.

Corollary 2.2 Let P be a normal cone, A : P h → P h be an increasing operator and B : P h → P h be a decreasing operator.

Corollary 2.8 Let P be a normal cone, A : P h → P h be an increasing operator and B : P h × P h → P h be a mixed monotone operator.

(A Krightarrow K) is an increasing operator.

Hence T is an increasing operator.

Therefore, T is an increasing operator.

Finally, we assert that is an increasing operator.

Hence maps into and is an increasing operator.