Sentence examples for proposition to show from inspiring English sources

Next we give the following proposition to show the description of the coderivative of some special set-valued mappings.

Before proposing our algorithm, we give a proposition to show the equivalences between (P) and ((mathrm{P}_{rho })).

This proposition shows that the choice is unique.

More recently, Qi, Zheng, and Sun [22 24] proved that case II and III depend on the corresponding half-planes by illustrating two examples and gave two propositions to show how case II and III depend on the corresponding half-planes.

Later, Samet et al. [63] established some propositions to show that many fixed point theorems on (nonsymmetric) G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces.

Let us use now Proposition 1.1 to show that (1.5) is satisfied too.

We aim to apply Part 1. of Proposition 1 to show existence and uniqueness of the solution to the 2BSDE (2BSDE

Next we use Proposition 4.8 to show the convergence analysis of Algorithm 4.1 under other control conditions.

Crescas's purpose in criticizing and rejecting several of these propositions was to show that the traditional Aristotelian proofs (founded in the first place on physical doctrines) were not valid.

The following technical proposition is needed to show an analogue to the main result in [25].

By Proposition 2.4(i), to show that x n ⇀ x, it suffices to show that w w ( x n ) ⊂ Γ.