Sentence examples for case of contraction from inspiring English sources

This question has been answered in the positive, in the case of contraction condition (1), by Ostrowski [2], who established the first stability result for a fixed point iteration procedure, by using the following estimate: d ( y n, p ) ≤ α n 1 − α d ( x 0, x 1 ) + ∑ k = 1 n α n − k ϵ k, n = 0, 1, 2, …, (2).

It is easy to prove that a pointwise contraction T : C → C has a fixed point in the same way as in the case of contractions.

However, in the case of contractions and in the case of dissipative operators one has to consider double operator integrals with respect to semi-spectral measures.

Prenatal testing is not indicated for the pregnant partner of a male with a premutation since only transmission of premutations have been reported in all the numerous daughters of such fathers, with some exceptional cases of contraction to an allele in intermediate or normal range, but in no case has there been an expansion to a full mutation.

Remark 2.1 Since each nonlinear contraction includes the case of linear contraction as its special case, each fixed point theorem in the above theorem implies a fixed point theorem for linear contraction.

As a result, cases of malaria and TB have declined in recent decades with cases of contractions amongst Bahraini nationals becoming rare.

Wardowski deduced that the Banach contractions are particular case of F-contractions and the author supported his finding by presenting some F-contractions which are not Banach contractions.

Sz.-Nagy's dilation theorem for a contraction on a Hilbert space has been extended by Mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group.

The stability of a fixed point iterative procedure was first studied by Ostrowski [17] in the case of Banach contraction mappings, and this subject was later developed for certain contractive definitions by several authors.

For instance, it is impossible to apply it in the case of isotonic contraction.

For instances, it is impossible to apply in the case of isotonic contraction.