In this work, we introduced and explored the concept of multiplicatively hyperbolic type convex functions, examining several of their fundamental algebraic properties. We established Hermite-Hadamard (HH) inequalities for this newly defined class of functions and further derived novel HH type inequali-ties for both the product and quotient of multiplicatively hyperbolic type convex functions. Furthermore, we obtained new multiplicative integral-based inequalities involving the product and quotient of multi-plicatively hyperbolic type convex functions and classical convex functions. In addition, by utilizing the Hölder-İşcan integral inequality, we developed several new HH type integral inequalities specifically for multiplicatively hyperbolic type convex functions. Finally, we conducted a comparative analysis with existing results, demonstrating that our findings offer notable improvements over previously known in-equalities. The results of this study have the potential to inspire further research in various scientific disciplines.
Serap Özcan (Wed,) studied this question.