Sentence examples for the equivalent relation from inspiring English sources

In this paper, a comparison of the two methods is stated, and the equivalent relation is further derived.

In addition, the equivalent relation between solutions of generalized Minty vector variational inequality and generalized vector-minimum points of vector optimization problems was shown.

Based on the weakly symmetric condition, Chang et al. [8] established the equivalent relation between the largest Z-eigenvalue and Z-spectral radius of nonnegative tensors.

In order to restrict SOC deviation to an acceptable level, the equivalent relation of the battery inconsistency caused by RICP to the inherent inconsistency is discussed.

As applications, we now generalize the Browder fixed point theorem to FC-spaces by using Corollary 3.4 and prove the equivalent relation between Browder fixed point theorem and Ky Fan's minimax inequality in FC-spaces without linear structure.

However, if (lim _{nto infty}e^{n(beta_{n}-alpha_{n})}=1) holds, then we have the equivalent relation (e^{nbeta_{n}}/nto0Leftrightarrow[n]_{p_{n},q_{n}}toinfty) from ((mathcal{A})).

Moreover, we give an example illustrating the equivalent relations.

The proof of the equivalent relations of, and can be found in [3].

The proof of the equivalent relations of can be found in [1, 2, 4, 5].

Using the equivalent relations, we obtain ε- optimality conditions for (weakly) ε- efficient solution for (MFP).

Consequently, from the equivalent relations of (mathcal{L}), L, (mathcal {E} ) and (3.8), we obtain the result in Theorem 3.1.