Some New Hermite-Hadamard Type Inequalities Pertaining to Fractional Integrals with an Exponential Kernel for Subadditive Functions

The class of symmetric function interacts extensively with other types of functions. One of these is the class of convex functions, which is closely related to the theory of symmetry. In this paper, we obtain some new fractional Hermite-Hadamard inequalities with an exponential kernel for subadditive functions and for their product, and some known results are recaptured. Moreover, using a new identity as an auxiliary result, we deduce several inequalities for subadditive functions pertaining to the new fractional integrals involving an exponential kernel. To validate the accuracy of our results, we offer some examples for suitable choices of subadditive functions and their graphical representations.

Automated summary

The class of symmetric function interacts extensively with other types of functions, particularly with convex functions. This paper presents new fractional Hermite-Hadamard inequalities with an exponential kernel for subadditive functions and their product, and it also recaptures some known results. Additionally, by using a new identity as an auxiliary result, several inequalities for subadditive functions involving new fractional integrals with an exponential kernel are deduced. The accuracy of the results is validated through examples and graphical representations of suitable choices of subadditive functions.