Sentence examples for on the mappings from inspiring English sources

Extensions of this principle were obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings [5 9].

Research along these lines is performed either by relaxing the assumptions on the mappings in the settings (for instance, commonly seen assumptions for the mapping involved in the fixed point problem are nonexpansive or strictly pseudocontractive) or by adding a general system of variational inequalities into the settings.

Extensions of the Banach contraction principle have been obtained either by generalizing the domain of the mapping (see, e.g., [1, 2]) or by extending the contractive condition on the mappings [3, 4].

In order to get strong convergence, Chang et al. [25] imposed a compactness-type condition (semi-compactness) on the mappings { S i } i = 1 ∞.

Under suitable conditions on the control parameters and without the assumption of semi-compactness on the mappings, a strong convergence theorem is established.

The novelty of our paper is the fact that we do not need differentiability, polynomial growth, or some integral conditions on the mappings and.

On the other hand, by reasoning on the properties of the mappings, the practice of coining weaker forms of commutativity to ensure the existence of a common fixed point for self-mappings on metric spaces is still on.

In particular we show the effect of dilatations on the Jacobian of the mappings which controls what is known as the crowding phenomenon in the literature.

Such information can only be gained via the direct analysis of the read sequences, instead of based on the statistics of the mappings of such reads.

on the Mapping 100K array was mapped according to the May 2004 genome assembly (hg17) at http://genome.ucsc.edu/ Single-nucleotide polymorphisms that did not map or mapped to more than one position in the genome assembly were excluded from the analysis, leaving 57 429 SNPs.

To address the issue of identifier heterogeneity, we have developed a SPARQL-based service that generates on-the-fly identifier mappings for registered IRI patterns.