Sentence examples for mappings in terms from inspiring English sources

Lim characterized this kind of mappings in terms of a contractivity condition using the following class of auxiliary functions.

Attapol Kaewkhao [8] has established FFP for multivalued nonexpansive mappings in terms of the James constant, the Jordan-von Neumann Constants, weak orthogonality.

In 2007, Domínguez Benavides and Gavira [7] have established FFP for multivalued nonexpansive mappings in terms of the modulus of squareness, universal infinite-dimensional modulus, and Opia modulus.

In [3], Barnett et al. pointed out a similar result to the above for twice differentiable mappings in terms of the upper and lower bounds of the second derivative.

However, so far, we have seen not many results for the approximation iteration of multivalued nonexpansive mappings in terms of Hausdorff metrics for fixed points in the existing literature.

The purpose of this paper is to extend the iteration scheme of multivalued nonexpansive mappings from a Banach space to a hyperbolic space by proving Δ-convergence theorems for two multivalued nonexpansive mappings in terms of mixed type iteration processes to approximate a common fixed point of two multivalued nonexpansive mappings in hyperbolic spaces.

Both Smt-MF and Smt-LF mappings were better than Std mapping in terms of resolving contours, especially in lower octaves (octave 3) with small (1-semitone) interval sizes, where Smt-LF mapping was statistically significant and this emphasizes that semitone mapping may be advantageous to the Std mapping.

In this paper, the PPF dependent fixed point theorems and the PPF dependent coincidence points for a pair of mappings are proven in terms of more general contractive conditions in Banach spaces.

Improved fine-mapping resolution, both in terms of the number of variants included in the credible sets and the genomic intervals they covered, was observed at all but one of the loci after trans-ethnic meta-analysis.

However, it is a well-known fact that all dimensionality reducing mappings have their problems in terms of displaying an unavoidable mapping error related to the intrinsic dimensionality of the data to be mapped as well as to the employed mapping method itself.

We also characterize the set of common solutions for families of total quasi-φ-asymptotically nonexpansive mappings and equilibrium problems in terms of Mosco convergence.