Sentence examples for basic lemma which is from inspiring English sources

We begin with the following basic lemma, which is one of the main tools for our results.

In order to obtain the existence of critical points of J on E, we cite the basic lemma, which is crucial in the proof of our main results.

Prior to giving some consequences as an application of this idea, we give the following basic lemma, which is the collection of the characterization of matrix transformations related to almost convergence.

The rest of the paper is organized as follows: In Section 2 we recall some preliminaries and present a basic lemma which is used to convert the impulsive fractional boundary-value problem (1.1) into an equivalent integral equation.

As a consequence, we obtain the following basic lemma which is instructive as to the bar construction of a module.

In Section 2, we prove some basic lemmas which are needed in succeeding sections.

In this section, we shall recall some basic definitions, lemmas which are used in what follows.

In this section, we shall first recall some basic definitions, lemmas which are used in what follows.

2, we recall some basic definitions and lemmas, which are based on the literature.

In this section, we first recall some basic definitions and lemmas which are used in what follows.

For the convenience of the readers, we present here some basic definitions and lemmas, which are used throughout this paper.