Sentence examples for Preparatory results from inspiring English sources

This section is devoted to some preparatory results.

A second point of interest emerges from the analysis of the preparatory results of this study.

The theorems of the following section require some preparatory results which we group together here.

In Section 4 we collect some preparatory results which will help us to simplify the proof of our main theorems.

The proof of the Theorem will be given at the end of this section after a long list of preparatory results.

The purpose of this section is to collect preparatory results which will help us to simplify the proof of both 'if' and 'only if' parts of our main theorems.

Now, we give the following important preparatory result.

First, we have the following preparatory result for later use.

The case when I is a finite set is straightforward, but the case when I is infinite, although it has a similar idea, requires a preparatory result, namely Lemma 4.6.

In this section, we show the convergence of the sequences {x n }, {y n } and {w n } defined by Algorithm 2.1 is based on the extragradient method and Armijo-type linesearch techniques which solves the problem of finding a common element of two sets ∩ i = 1 p Fix S i and Sol f, C. To prove it's convergence, we need the following preparatory result.

In Section 3, the reader can find preparatory lemmas, results, and corollaries.