Sentence examples for mappings is very from inspiring English sources

Fixed point theory of nonexpansive and noncommuting mappings is very rich in Banach spaces and metric spaces [13 17].

The fixed point theory for such mappings is very rich [5 9] and has many applications in nonlinear functional analysis [10].

Therefore, Bregman quasi-Lipschitz mappings are very important in the nonlinear analysis and fixed point theory and applications.

It is a well-known fact that the mathematical results regarding fixed points of contraction-type mappings are very useful for determining the existence and uniqueness of solutions to various mathematical models.

Generally, results from multiple trait mappings were very similar to those from the single trait analysis except that fewer false positives were detected (results not shown).

Adding HLA amino-acid variants and classic alleles in a fine-mapping study is very important for better localization of association effects to precise variants because the identification of primary and secondary effects highly depends on adjusting factors used in a conditional analysis.

However, the study of the existence of common fixed points for noncompatible mappings is, also, very interesting.

On the other hand, the study of existence of fixed points for non-self mappings is a very interesting.

The study of expansive mappings is a very interesting research area in fixed point theory (see [19, 21 23]).

Define D s : X 2 → [ 0, ∞ ) by D s ( x, y ) = | 2 D ( x, y ) − D ( x, x ) − D ( y, y ) |. Clearly, D s ( x, x ) = 0 for all x ∈ X. The study of expansive mappings is a very interesting research area in fixed point theory (see, e.g., [14 21]).

Importantly, the mapper can provide one-to-one mappings between species, which is very useful during analysis.