Analysis On Perturbed Hermite-Hadamard Type Inequalities Through Convexity Classes and Their Applications

This research contributes to the field of mathematical inequalities by extending Hermite-Hadamard-type inequality results to the fractional calculus. We introduce novel Hermite-Hadamard-type inequalities that incorporate Riemann-Liouville fractional integrals, utilizing convex and tgs -convex functions. Several significant estimates for these new inequalities are derived, and graphical representations to enhance the understanding of the results are obtained. Additionally, the study explores applications to various special means of real numbers, the modified Bessel function, and the q-digamma function.

Keywords:

Hermite-Hadamard inequality , convex function , tgs-convex function , Hölder’s inequality , power-mean inequality , Special means , Modified Bessel function , q-digamma function