Sentence examples for mapping and hence from inspiring English sources

We observe from (1.1), (1.2) and (1.3) that every nonexpansive mapping is an α-strictly pseudocontractive mapping and every α-strictly pseudocontractive mapping is a pseudocontractive mapping, and hence a class of pseudocontractive mappings is a more general class of mappings.

The main objective of the survey was to highlight the applicability, efficiency, and reliability of utilizing such non-invasive surface techniques in a field like geologic mapping, and hence to image both the vertical and lateral electrical resistivity structures of the subsurface bedrock.

and the mapping, and hence, generates a Nemytskii operator by (3.12).

This implies that is a contraction mapping and hence the conclusion follows.

Thus, T is nonexpansive mapping and hence it satisfies condition (C).

Now by [21, Lemma  2.4], is a linear mapping and hence is a linear mapping.

The next example motivates the study of multivalued mappings by showing that control problems may be translated in terms of multivalued maps and, hence, a study of their fixed points could provide new solution schemes to such problems.

If set to NONE then the instrument map, and hence exposure map, will be created with no bad pixels.

Our results underline the importance of the in-host environment in determining bacterial genotype-fitness maps, and hence the necessity of carefully-designed lab models (Roberts et al., 2015).

The relevant articles in blogs are used to promote learner engagement in their interactions with the learning map and hence achieve their goals more easily.

The method is formulated to design a heat sink for an arbitrary chip power map and hence can be readily utilized for different chip architectures.