Xuexiao YouMuhammad Aamir AliHŸseyin BudakJiraporn ReunsumritThanin Sitthiwirattham2025-03-102025-03-102021Mathematics2227739010.3390/math92025562-s2.0-85117443024https://repository.dusit.ac.th//handle/123456789/4701In this paper, we prove HermiteÐHadamardÐMercer inequalities, which is a new version of the HermiteÐHadamard inequalities for harmonically convex functions. We also prove HermiteÐ HadamardÐMercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.All Open Access; Gold Open AccessHarmonically convex functionHermiteÐHadamardÐMercer inequalityJensen inequalityArticleScopus