Sentence examples for space convergence from inspiring English sources

We recall some concepts from probabilistic metric space, convergence and contraction.

By means of the decomposition in a Clifford-valued function space, convergence of the very weak solutions to A-Dirac equations is obtained in Clifford analysis.

If ( V 2, ν ′, τ 2, τ 2 * ) is an α-Šerstnev PN space, then ( L ( V 1, V 2 ), ν A, τ 2, τ 2 * ) is an α-Šerstnev PN space; convergence in the probabilistic norm ν A is equivalent to uniform convergence of operators on A. Proof.

In such a space, convergence of sequences is defined in the usual way: A sequence { x n } ⊆ X is said to converge to x ∈ X if lim n → ∞ d ( x n, x ) = 0. Also, a sequence is said to be Cauchy (or d-Cauchy) if for each ε > 0 there exists N ∈ N such that m, n ≥ N ⇒ d ( x m, x n ) < ε.

When the estimates are not on the boundary of the parameter space, convergence problems may still happen, and better starting values for the estimation process than the default used by the software will help.

In the context of modular function spaces, convergence to fixed points of some iterative algorithms, applied to asymptotic pointwise nonexpansive mappings, was proven by Bin Dehaish and Kozlowski in [22].

In a CAT 0) space, strong convergence implies convergence and they are coincided when is a Hilbert space.

A vector space with convergence Y endowed with vector ordering is called an ordered vector space with convergence.

An interesting consequence in probability space is convergence in probability of all continuous functions on every convergent in probability sequence.

A vector space with convergence ( Y, → ) equipped with a vector ordering ⪯ is called an ordered vector space with convergence and is denoted by ( Y, ⪯, → ).

In Section 4, we introduce the definition of an ordered vector space with convergence and the well-known theorem that the vector orderings and cones in a vector space with convergence are in one-to-one correspondence.