Sentence examples for contraction relation from inspiring English sources
Using the contraction relation we can find p2 ∈ fp1 such that F p 1 p 2 > 1 - φ , and by induction, p n such that p n ∈ fpn-1and F p n - 1 p n ( ψ n - 1 > 1 - φ n - 1 for all n ≥ 1. Defining t n = ψ n, we have g j = F p j p j + 1 ( t j ) ≥ 1 - φ j , ∀j, so lim n → ∞ ⊤ i = 1 ∞ g n + i - 1 ≥ lim n → ∞ ⊤ i = 1 ∞ ( 1 - φ n + i - 1 = 1.
Conditions preserving closed-loop systems expansion-contraction relations including the identical bounds of performance indices are proved.
Conditions preserving closed-loop systems expansion-contraction relations including the equality of bounds of costs are proved.
They are called cross bridges and are believed to be responsible for the movement and force developed during contraction (for the relation of cross bridges to the molecular architecture of thick filaments, see below).
Phasic contraction is modeled in relation to the time constant of changing <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0018685.e014.PNG" class= inline-graphic"/>.
The decrease in contraction was calculated in relation to the contractions just before toxin addition.
Most recently, Alam and Imdad [23, 24] established a new relation-theoretic version of the Banach contraction principle employing general binary relation which in turn generalizes several well known relevant order-theoretic fixed point theorems.
In [21], Berinde obtained some constructive fixed point theorems for almost contractions satisfying an implicit relation.
For applications of contraction principles to variational relations, the reader is referred to [4].
In this paper, we base our methodology on another theorem proven in the field of crystallizations, which puts in relation dipole contractions and the connected sum of manifolds.
As applications of our theorems, we derive some new best proximity point results for implicit relation type contractions whenever the range space is endowed with a graph or with a partial order.
