<p>In this paper, we take into account the notion of strongly multiplicative convex function and derive integral inequalities of Hermite-Hadamard ($ H.H $) type for such a function in the frame of multiplicative calculus. We also develop integral inequalities of $ H.H $ type for product and quotient of strongly multiplicative convex and strongly multiplicative concave functions via multiplicative calculus. All the results of the theorems are verified graphically by taking into account some reasonable examples. Additionally, we establish the inequalities of the Milne type for strongly multiplicative convex functions.</p>