Sentence examples similar to exists is increasing from inspiring English sources

Assume that there exists, such that is increasing and (2.3).

According to Definition 2.3 there exists, such that is increasing and (2.3) holds.

Since for some there exists such that is increasing on for some, positive, differentiable and obeys as.

(i for each with there exists such that and ; (ii) is increasing; (iii there exists such that ; (iv).

By (H), when (E(n+1)>0) exists, then (Phi(x)) is increasing for (xgeq0).

Also, because is regularly varying at infinity with index, there exists a function which is increasing and which obeys as.

In particular we prove that for each sufficiently small there exists a solution such that is increasing, and.

Since x ∗ ∈ g ( X ) and g is increasing, there exists a unique s ∈ X such that g ( s ) = x ∗.

Because of (3.22) and the fact that is increasing, there exists a function such that converges pointwise on to.

Since k is increasing, there exists the inverse function k − 1 and we can write t ∗ ≤ k − 1 ( ( Ψ ( 0 ) ) 1 − q q − 1 ), which is the desired upper bound of t ∗.

Next, since h is increasing, (h^{-1}) exists and is an increasing function.