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The Hermite-Hadamard integral inequality is one of the most well-known integral inequalities in the theory of convex functions. This article contributes to the subject by examining the Hermite-Hadamard integral inequality in the context of inverse functions. In addition, alternative proofs are presented to highlight the subtlety and complexity of the problem.

convex functions, concave functions, Hermite-Hadamard integral inequality, Young integral inequality.