Modified class of hyperbolic p-convex function with application to integral inequalities

In this paper, the new class of modified hyperbolic p-convex functions is introduced and some of their basic algebraic properties are presented. The motivation behind for introducing this new class is that it can solve more complicated problems, such as those with hyperbolic structures and fractional calculus, which are often inadequately handled by classical convex functions. By utilizing this modified class, some new integral inequalities related to the Hermite-Hadamard (H-H) inequality are derived. A particular identity for differentiable functions is also used that enables an extension and improvement of the classical H-H inequality. This work explores the relationships between these modified hyperbolic p- convex functions and other classes of convex functions, demonstrating the superiority of the newly obtained inequalities over previous findings. Finally, several examples with graphs are provided to illustrate the validity of the newly established inequalities, and a comparison with earlier results highlights their enhanced applicability and significance.