Sentence examples for be a decreasing and from inspiring English sources

Theorem 2.1 Let E be an ordered Banach space with lattice structure, D ⊂ E be bounded, and A : D ⟶ D be a decreasing and condensing operator.

Theorem 2.2 Let E be an ordered Banach space with lattice structure, P ⊂ E be a normal cone, and A : E ⟶ E be a decreasing and condensing operator.

Corollary 3.1 Let E be an ordered Banach space with lattice structure, D ⊂ E be bounded, and A : D ⟶ D be a decreasing and completely continuous operator.

Then the operator A has a fixed point in D. Corollary 3.2 Let E be an ordered Banach space with lattice structure, P ⊂ E be a normal cone, and A : E ⟶ E be a decreasing and completely continuous operator.

Then the operator A has a fixed point in E. Corollary 3.3 Let E be an ordered Banach space with lattice structure, D ⊂ E be bounded, and A : D ⟶ D be a decreasing and strict-set-contraction mapping.

(a) Let G : [ 0, ∞ ) → [ 0, ∞ ) be a decreasing and log-convex function, with G ( x ) > 0, x ≥ 0 and right-continuous at x = 0. Then E G [ X ( t ) ] is a log-convex function on [ 0, ∞ ).

"There has to be a decrease, and at best an end, to cross-border attacks by Taliban and Al Qaeda people from Pakistan.

But the decrease--0.6 percent--is so small that it may not be a decrease and could actually be a slight increase because of the margin of error.

The yield differential between notes and bills is a decreasing and convex function of the time to maturity.

Then, is a decreasing and bounded below sequence, and hence there exist such that.

Therefore is a decreasing and bounded below sequence,and there exists such that.