Sentence examples for consequence of the corresponding from inspiring English sources

Moreover, our results cannot be directly obtained as a consequence of the corresponding results in metric spaces.

In 2011, Janković et al. [24] showed that most of the fixed point results in the set-up of normal cone metric space can be obtained as a consequence of the corresponding results in metric spaces.

As system (2.1) is quasilinear with each of these equations being a direct consequence of the corresponding conservation law, one expects shocks to appear in the flow after a finite running length or time.

This shows that one is unable to prove that Theorem 2.1 above is a consequence of the corresponding results in metric spaces by means of the methods presented in the literature.

Differences in equipment costs (858 US$ - 2,509 US$) are mainly the consequence of the corresponding age of the institution, as expensive inventory is normally transferred at the date of opening the facility.

Namely, by using the properties either of the Minkowski functional (q_{e}) or the nonlinear scalarization function (xi_{e}) (in particular their monotonicity), some scholars have made a conclusion that many fixed point results in the setting of cone metric spaces or tvs-cone metric spaces can be directly obtained as a consequence of the corresponding results in metric spaces (see [1 12]).

And then we will obtain new results on the existence and uniqueness of positive solutions for these problems, which are not consequences of the corresponding fixed point theorems in the literature.

In this note we prove that the topology τ generated by an intuitionistic fuzzy normed space ( X, μ, ν, ∗, ⋄ ) coincides with the topology τ μ generated by the generalized fuzzy normed space ( X, μ, ∗ ), and thus, the results obtained in [5] and [6] are immediate consequences of the corresponding results for fuzzy normed spaces.

In [4] Saadati and Park proved that the topology τ generated by an intuitionistic fuzzy normed space ( X, μ, ν, ∗, ⋄ ) coincides with the topology τ μ generated by the generalized fuzzy normed space ( X, μ, ∗ ), and thus the results obtained in intuitionistic fuzzy normed spaces are immediate consequences of the corresponding results for fuzzy normed spaces.

Saadati and Park proved that the topology τ generated by an intuitionistic fuzzy normed space ( X, μ, ν, ∗, ⋄ ) coincides with the topology τ μ generated by the generalized fuzzy normed space ( X, μ, ∗ ), and thus the results obtained in intuitionistic fuzzy normed spaces are immediate consequences of the corresponding results for fuzzy normed spaces.

In 2011, Haghi et al. [11] proved a powerful lemma and showed that some coincidence and common fixed point generalizations in fixed point theory are merely consequences of the corresponding fixed point theorems existing in the literature (for more details, see [11]).