Sentence examples for be a continuous nondecreasing from inspiring English sources

Let (rho R^rightarrow R^) be a continuous nondecreasing function.

Let f : X → X be a continuous nondecreasing mapping.

Let,, be nonnegative continuous functions defined on, and let be a continuous nondecreasing function on with for.

and let X ( t ) be a continuous nondecreasing map from the real interval [ a, b ] to the interval I ⊂ R k.

Let (h:[0,infty)rightarrow[0,infty)) be a continuous nondecreasing function such that (int_{0}^{infty}{1/(1+h(r))},dr=+infty). Let ({mathcal {M}}) be a complete metric space and (x_{0}) be a fixed point of ({mathcal {M}}). Suppose that (f:{mathcal {M}}rightarrow mathbb {R}cup{+infty}) is a lower semicontinuous function, not identically +∞, bounded from below.

We can state the classical Borel [1] lemma for bivariate functions as follows: Let T be a continuous nondecreasing function on ([r_{0}, infty )times [s_{0}, infty )) for some (r_{0}) and (s_{0}) such that (T (r_{0},s_{0}) ge 1).

We consider equations (E) −Δu+g u)="μ in smooth bounded domains Ω⊂RN, where g is a continuous nondecreasing function and μ is a finite measure in Ω.

where is a continuous nondecreasing function for all with.

(H*1) There is a continuous nondecreasing function such that for all and.

where,, and are all constants,, and are both nonnegative real-valued functions defined on a lattice in, and is a continuous nondecreasing function satisfying for all.

Let Ψ be the set of all functions ψ where ψ : [ 0, + ∞ ) → [ 0, + ∞ ) is a continuous nondecreasing function with ψ ( t ) < t for all t ∈ ( 0, + ∞ ) and ψ ( 0 ) = 0. If ψ ∈ Ψ, then ψ is called a Ψ-map.