Sentence examples for be a nondecreasing continuous from inspiring English sources

Let be a nondecreasing continuous function, and let be the set of all such that (3.10).

Lemma 2.3 Let T : [ 0, ∞ ) → [ 0, ∞ ) be a nondecreasing continuous function, and s ∈ ( 0, ∞ ).

Let (g u)) be a nondecreasing continuous function defined on (mathbf{R}_) with (g u)>0) for (u>0).

Let Ω be a smooth domain of ({mathbb{R}}^{n}) ((ngeq1)) and (f:[0,infty) rightarrow 0,infty)) be a nondecreasing continuous function.

Theorem 2.5 Let X be a nondecreasing continuous map from the real interval [ a, b ] into an interval I ⊂ R k, and let H be a function of bounded variation on [ a, b ] with H ( a ) = 0. Then ∫ a b f ( X ( t ) ) d H ( t ) ≥ 0 (8).

Then ρ2 is a nondecreasing continuous function such that ρ2 0) = 0.

is an fw-distance on ( X, M, ∗ ), where d ( t ) is a nondecreasing continuous function with 0 < d ( t ) < c ( t ).

We study the existence of solutions of the nonlinear problem 0.1 -Δu+g u)="0inΩ,u="μon∂Ω,where μ is a bounded measure and g:R→R is a nondecreasing continuous function with g(t)="0, ∀t⩽0.

Assume that A : P → P is a nondecreasing, continuous and subadditive (i.e., A ( u + v ) ⪯ A u + A v for each u, v ∈ P ) mapping with A θ = θ such that ∑ i = 0 ∞ ∥ A i u ∥ < ∞, ∀ u ∈ P. (2).

We prove in this paper that if f is a nondecreasing continuous function on R that vanishes on (−∞,0] and is concave on [0,∞), then its operator modulus of continuity Ωf admits the estimateΩf⩽const∞∫ef δt dtt2logt,δ>0. We also study the problem of sharpness of estimates obtained in Aleksandrov and Peller (2010) [2], [3].

Assume that (0is a nondecreasing continuous function with (psi_{i} u)>0) for (u>0), (i=1,2).