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The aim of this paper is to obtain some new Hermite–Hadamard type of inequalities via harmonic convex, strongly harmonic convex, strongly harmonic <inline-formula> <tex-math notation="LaTeX">$\log $ </tex-math></inline-formula>-convex functions, and <inline-formula> <tex-math notation="LaTeX">$AH$ </tex-math></inline-formula>-convex in connection with quantum calculus. All the results reduce to ordinary calculus case when <inline-formula> <tex-math notation="LaTeX">$q\to 1^{-}$ </tex-math></inline-formula>.

New Quantum Hermite-Hadamard Inequalities Utilizing Harmonic Convexity of the Functions