On Hermite-Hadamard-type inequalities for systems of partial differential inequalities in the plane-Reference-Cited by-同舟云学术

On Hermite-Hadamard-type inequalities for systems of partial differential inequalities in the plane

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Jleli Mohamed¹,Samet Bessem¹

Affiliation:

1. Department of Mathematics, College of Science, King Saud University , P.O. Box 2455 , Riyadh, 11451 , Saudi Arabia

Abstract

Abstract We establish necessary conditions for the existence of solutions to various systems of partial differential inequalities in the plane. The obtained conditions provide new Hermite-Hadamard-type inequalities for differentiable functions in the plane. In particular, we obtain a refinement of an inequality due to Dragomir [On the Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwan. J. Math. 5 (2001), no. 4, 775–788] for convex functions on the coordinates.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0115/pdf

Reference20 articles.

1. C. Hermite, Sur deux limites daune intégrale défine, Mathesis 3 (1883), 82.

2. J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier daune fonction considérée par Riemann, J. Math. Pures Appl. 9 (1893), 171–215.

3. L. Fejér, Über die Fourierreihen, II, Math. Naturwiss, Anz. Ungar. Akad. Wiss. 24 (1906), 369–390.

4. S. Abramovich and L. E. Persson, Fejér and Hermite-Hadamard type inequalities for N-quasiconvex functions, Math. Notes 102 (2017), 599–609.

5. P. Cerone and S. S. Dragomir, Mathematical Inequalities, A Perspective, CRC Press, London, 2010.