Sentence examples for be a decreasing operator from inspiring English sources

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

An operator (A: Cto X) is said to be a decreasing operator if x,yin C,quad xpreceq yquad Longrightarrowquad Axsucceq Ay.

Theorem 2.12 Let P be a normal cone, A : P → P be a decreasing operator and B : P × P → P be a mixed monotone operator.

Let A : P → P be a decreasing operator which satisfies (H31), operators B 1, B 2 be the same as for Corollary  2.9.

Let A 1 : P → P be an increasing α-concave operator and A 2 : P → P be an increasing sub-homogeneous operator, B : P → P be a decreasing operator which satisfies (2.3).

Thus A is a decreasing operator.

Since A is a decreasing operator, we have A 2 x ≤ A u 0, A x ≤ A u 0. (2.9).

Since A is a decreasing operator, we have A v 0 ≤ A 2 x, A v 0 ≤ A x. (2.5).

In this paper we study a class of sum operator equation (Ax+Bx+C x,x =x) on ordered Banach spaces, where A is an increasing operator, B is a decreasing operator, and C is a mixed monotone operator.

Here, the operator (A Prightarrow P) is an increasing, (B Prightarrow P) is a decreasing operator, (C Ptimes Prightarrow P) is a mixed monotone operator.