Sentence examples for mappings as in from inspiring English sources

Let be the same mappings as in the previous case.

Let be two ordinary set-valued mappings, and let be the mappings as in problem (2.5).

Using the mentioned properties for Ψ 1 and Ψ 2, we prove the analogous PPF dependent fixed point theorems for mappings as in Drici et al. (Nonlinear Anal.

Using the mentioned properties for Ψ 1 and Ψ 2, we prove the analogous PPF dependent fixed point theorems for mappings as in [2] in partially ordered real Banach spaces where mappings satisfy the weaker contractive conditions.

Is there some way to improve the results to more than two mappings or a family of mappings as in the case of nonexpansive mappings (see, for example, [10] and references contained therein)?

Questions (i) Are the results in Theorem 2.2 and Theorem 3.4 still true when the norm closedness for R c is replaced by weak closedness or weak∗ closedness (for dual Banach spaces)?   (ii) Is there some way to improve the results to more than two mappings or a family of mappings as in the case of nonexpansive mappings (see, for example, [10] and references contained therein)?  .

This generalization is in line with Edelstein's generalization of Meir-Keeler type mappings, as well as in line with the recent one used in (Eshaghi Gordji in Math. Probl. Eng. 2012 150363, 2012).

To find support for miRNA expression, we downloaded all ESTs and and cDNAs mapped to mouse genome assembly NCBI 36 from the UCSC Genome Browser Database [61] in September 2006 and processed the mappings as described in [71] to remove low-quality sequences, reliably assign sequences to a genomic strand, and merge sequences obtained from the same cDNA clone.

The global information applied in the proposed method helps establish reliable mappings as shown in Fig. 1 a, since it effectively compensates the insufficiency of the distinctiveness of the descriptors.

It iswell known that the Opial property and normal structure of a Banach space Xplay an important role in metric fixed point theory for nonexpansive mappings, as wellas in the theory of differential and integral equations (see [1, 4 6]).

The output was generated by the NAO robot playing the theremin with the parameter mappings as shown in Table 4.