Two new extensions of Hardy-Hilbert-type integral inequalities

Abstract

In this paper, we investigate two new Hardy-Hilbert-type integral inequalities that incorporate both the maximum and the sum of the variables within the integrands. The second inequality is presented as a three-dimensional analogue of the first. Our proofs rely on the H\"older integral inequality and various integral identities. Finally, the paper concludes by posing a related open problem.