Sentence examples for mappings we also from inspiring English sources

By using the generalized resolvent operator technique associated with (A, η -accretive mappings, we also prove the existence of solutions for a class of generalized nonlinear relaxed cocoercive operator equation systems and the variational convergence of the sequence generated by the perturbed iterative algorithm in q-uniformly smooth Banach spaces.

Firstly, the underlying set that we considered is a Banach lattice; secondly, besides the case of upper ≽-preserving set-valued mappings, we also examine the fixed point theorems for lower ≽-preserving set-valued mappings; finally, our results do not require the domain C to be convex, and it is easy to construct this kind of examples.

For fine-mapping, we also used the so-called LCN near isogenics lines [ 17].

In Theorem 3.1, as S and T are two nonexpansive mappings, demi-contractive mappings or asymptotically strict pseudocontraction mappings, we can also obtain similar results.

(5) For several iterative schemes based on hybrid steepest-descent method for generalized mixed equilibrium problems, variational inequality problems, and fixed point problems for strictly pseudocontractive mappings, we can also refer to [26 32] and the references therein.

As applications, we prove the existence of the solutions for two types of random quasi-variational inequalities with random fuzzy mappings, and we also obtain random fixed point theorems.

Apart from continued fine-mapping, we will also use transcriptome sequencing and association mapping to confirm the candidate gene for qRgls2.

For this reason, in addition to using the gene mappings between genomes, we also looked at the evolutionary trees generated by PHRINGE, which provide the actual evolutionary history of the genes and facilitate the accurate determination of orthology by analyzing gene duplications and losses.

By Lemma 5.5, lim n → ∞ | | x n - x ̄ | | = 0. Furthermore, since T1 and T2 are nonexpan-sive mappings, we know that x ̄ is also a fixed point of T1 and T2.

We then consider multivalued mappings in Section 4. We also show in this section that the converse of Theorem 1.4 is true.

It is worth pointing out that many theorems in some corresponding published papers cannot be applied to this example since Theorem 3.1 does not require any condition on the containment of the ranges of involved mappings, and in this example we also do not require such containment.