Sentence examples for mappings that includes from inspiring English sources

The paper deals with a class of contracting mappings that includes the Boyd-Wong and the Matkowski classes.

If (u_{n}equiv0) and (v_{n}equiv0) for all (ngeq1), we obtain from (1.6) the class of mappings that includes the class of Bregman quasi-nonexpansive mappings.

If μ n = 0 and l n = 0 for all n ≥ 1, we obtain from (1.5) the class of mappings that includes the class of nonexpansive mappings.

Mapping studies that include many individuals in the analysis necessitate the production of large numbers of genotypes.

These data can be properly interpreted only using a metabolic model that includes information about atom mappings for each reaction (Zupke & Stephanopoulos, 1994; Wiechert et al., 1999; Antoniewicz et al., 2007a).

Gene reconstructions that include these sequence-mapping problems are marked as incomplete in the results section of Kassiopeia.

The limitations of this work include the following: The mappings that we have performed may contain errors, or be disputed by others.

The class of quasi-nonexpansive mappings and asymptotically nonexpansive mappings includes nonexpansive mappings, where as the class of asymptotically quasi-nonexpansive mappings is larger than that of quasi-nonexpansive mappings and asymptotically nonexpansive mappings.

They defined the notion of α-ψ contractive mappings and proved that including the Banach fixed point theorems, some well-known fixed point results turn into corollaries of their results.

It worth noting that the class of generalized strictly pseudocontractive mappings includes generalized Lipschizian mappings, λ-strictly pseudocontractive mappings, λ-Lipschitzian mappings, pseudocontractive mappings, nonexpansive (or 0-strictly pseudocontractive) mappings.

Remark 2.1 It is clear that the class of asymptotically nonexpansive mappings includes nonexpansive mappings, whereas the class of asymptotically nonexpansive mappings in the intermediate sense is larger than that of asymptotically nonexpansive mappings.