Discussions on two integral inequalities of Hermite-Hadamard type for convex functions

In the paper, the authors, (1) by constructing a counterexample and utilizing Minkowski's inequality, demonstrate that there existed errors in the proofs of Theorems 1 and 2 in the paper Mehrez and Agarwal, (2019); (2) with the help of an integral identity and by means of Holder's integral inequality, present a new integral inequality of the Hermite-Hadamard type for convex functions. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this paper, the authors demonstrate the errors in the proofs of Theorems 1 and 2 in a previous paper by constructing a counterexample and utilizing Minkowski's inequality. They also present a new integral inequality of the Hermite-Hadamard type for convex functions using an integral identity and Holder's integral inequality.