Multiplicatively Hyperbolic Type Convex Functions and Some Related Integral Inequalities

Abstract

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 inequalities 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 multiplicatively hyperbolic type convex functions and classical convex functions. In addition, by utilizing the Holder–Iscan 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 inequalities. The results of this study have the potential to inspire further research in various scientific disciplines.