Superquadratic function and its applications in information theory via interval calculus

The goal of this study is to introduce a new class of superquadraticity, which is known as superquadratic interval valued function (superquadratic I-V-F) and establish its properties via order relations of intervals. By utilizing the definitions and properties of superquadratic I-V-F, we come up with new integral inequalities such that Jensen’s, converse Jensen’s, Mercer Jensen’s and Hermite–Hadamard types. In addition to this, we provide a fractional version of Hermite–Hadamard’s type inequalities for superquadratic I-V-Fs. The findings are validated by specific numerical computations and graphical illustrations that include a certain number of relevant examples. We also offer the applications of the established results in information theory such that we determine the novel estimates for Shannon’s and relative entropies.