Sentence examples for the third inequality of from inspiring English sources

For the third inequality of Proposition 3.

(ii) For the third inequality of Proposition 3.

Compare with the third inequality of (2.5), we have (2.7).

The third inequality holds due to Theorem 2.1 (or the third inequality of (12)).

To prove the third inequality of (18), it is sufficient to prove the following inequality: t m − 1 + ⋯ + t + 1 ≤ m ( t m − 1 + 1 ) 2 ( t > 0 ).

If,,, (3.4) becomes the second inequality of (1.1) with and, and the third inequality of (1.1) with and, which are discussed in the book [21].

The solution corresponds to that one of the second and the third inequalities of (7) achieves equality.

which contradicts the first inequality of (11).

This gives the second inequality of the assertion.

which implies the first inequality of the claim.

The first inequality of (1.1) is the classical Young inequality.