Sentence examples for be an increasing mapping from inspiring English sources

Let f : X → X be an increasing mapping such that there exists x0 ∈ X with x0 ≤ f (x0).

Let (P:=(P,preccurlyeq )) be a partially ordered set and f be an increasing mapping from P into P.

Let f be an increasing mapping of a partially ordered metric space (X:= X,preccurlyeq,rho)) into itself.

Let f be an increasing mapping of a partially ordered transversal upper edges space (X:= X,preccurlyeq,rho)) into itself.

Let F : R + → R be an increasing mapping and { α n } n = 1 ∞ be a sequence of positive real numbers.

Let f be an increasing mapping of a partially ordered transversal lower edges space (X:= X,preccurlyeq,rho)) into itself.

Lemma 3.2 Let F : R + → R be an increasing map and ( t k ) k be a sequence of positive real numbers.

Assume that F X × X → → X be an increasing map with respect to ⪯ and there exist two elements x 0, y 0 ∈ X with x 0 ⪯ F ( x 0, y 0 ) and y 0 ⪰ F ( y 0, x 0 ).

T is an increasing mapping, there is (x_{0}in X) such that (x_{0}preceq Tx_{0}), T is continuous or, X is regular.

Showing that F is an increasing mapping can be done by the definition, that is, if (x_{1}leq x_{2}), then (Fx_{1}leq Fx_{2}).

As claimed in the previous theorem, it can be verified that ((Y,leq)) is a complete lattice and F is an increasing mapping.