Properties and integral inequalities of P-superquadratic functions via multiplicative calculus with applications

Abstract This manuscript explores the idea of a multiplicatively P-superquadratic function and its properties. Utilizing these properties, we derive the inequalities of Hermite–Hadamard type for such functions in the framework of multiplicative calculus. In addition to this, we derive integral inequalities of Hermite–Hadamard type for the product and quotient of multiplicatively P-superquadratic and multiplicatively P-subquadratic functions. Moreover, we develop the fractional version of Hermite–Hadamard type inequalities involving midpoints and end points for multiplicatively P-superquadratic functions with respect to multiplicatively Riemann–Liouville (R.L) fractional integrals. Graphical illustrations based on specific relevant examples validate the credibility of the findings. The study is further stimulating by being pushed with potential applications in terms of moment of random variables, special means, and modified Bessel functions of the first kind. Regarding superquadraticity, the results presented in this work are new, therefore they clearly provide extensions and improvements of the work available in the literature.