Fractal Hadamard–mercer-Type Inequalities With Applications

Fractal analysis is a totally new area of research based on local fractional calculus. It has interesting applications in various fields such as a complex graph, computer graphics, the music industry, picture compression and many more fields. In this paper, we present new variants of Hadamard–Mercer-type inequalities on fractal sets [Formula: see text] ([Formula: see text] by employing generalized convex function. We establish two new lemmas involving local fractional integrals. By using these lemmas, we obtain several results related to generalized Hadamard–Mercer-type integral inequalities for local differentiable generalized convex functions on real linear fractal space. Finally, we give applications for probability density functions and compute new generalized means.