Jiraporn ReunsumritMiguel J. Vivas-CortezMuhammad Aamir AliThanin Sitthiwirattham2025-03-102025-03-102022Symmetry2073899410.3390/sym140203022-s2.0-85124101556https://repository.dusit.ac.th//handle/123456789/4597In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.All Open Access; Gold Open AccessHarmonically convex functionsMidpoint and trapezoidal inequalitySimpsonÕs inequalityArticleScopus