<p>We study the concept of multiplicative harmonic <i>s</i>-convex functions and establish Hermite–Hadamard integral inequalities for this class of functions. Furthermore, we obtain a set of Hermite–Hadamard-type inequalities applicable to the products and quotients of multiplicative harmonic <i>s</i>-convex functions. In addition, we deduce new inequalities involving multiplicative integrals for the products and quotients of harmonic convex and multiplicative harmonic <i>s</i>-convex functions. Some results for the class of multiplicative harmonic convex functions are obtained as special cases of our results. The obtained results are verified by the presented examples with included graphs.</p>