Multiplicatively h‐Superquadratic Functions and Their Applications in Probability, Special Functions, and Means

ABSTRACT In this manuscript we first time introduce the notion of a multiplicatively ‐superquadratic function and present its properties. These properties serve as the foundation for the derivation of H.H's (Hermite–Hadamard's) type inequalities via multiplicative calculus. Additionally, we established H.H's type inequalities for both the product and quotient of multiplicatively ‐superquadratic functions and standard superquadratic functions within the framework of multiplicative calculus. We also provide some new definitions, such as multiplicatively s‐superquadratic function and multiplicatively superquadratic functions of the Godunova‐Levin type. By using different substitutions for the function , such that , and in the obtained results, we get the novel results for multiplicatively superquadratic functions, multiplicatively s‐superquadratic functions and multiplicatively superquadratic functions of the Godunova‐Levin type, respectively. The results are validated through two‐ and three‐dimensional visual illustrations based on appropriate examples. An additional driving force behind the research is the addition of applications concerning the moment of random variables, modified Bessel functions of type‐1 and special means. The results presented in this work are novel within the framework of superquadraticity and multiplicative calculus. Without any doubt, this will have major implications for the development of additional research.