Sentence examples for extend this inequality from inspiring English sources

We can extend this inequality to matrices as follows: (2.35).

One can note that the inequality (2.23) has been proved without weighted functions, so it will be interesting to extend this inequality and prove an inequality similar to the inequality (2.23) with weighted functions.

For more recent results which generalize, improve and extend this classical Hermite-Hadamard inequality, one can see [3 13] and references therein.

The purpose of this paper is to extend the inequality (1.4) to the higher dimensional cases (ngeq1) in terms of the Lorentz-Zygmund type spaces in (mathbb{R}^{n}).

In the next proposition, we extend the inequality (A.1) to cover the case.

Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.

The problem is to extend the inequalities (15), (19), (23), (28) and (29) for QR-submanifolds in quaternionic space forms.

In this way, Jensen (see [1]) has extended the inequality in equation (1.2).

For the contribution on the recent results which generalized, improved, and extended this classical Hermite-Hadamard inequality via convex functions, we refer the reader to [2 16] and references therein.

Jensen (see [1]) extended the inequality in equation (2) by relying on induction.

Recently, the author of this paper gives a new proof of the inequality (1.1) in [3] and extends the inequality (1.1) to the following result in [4].