Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals

Year 2025, Volume: 8 Issue: 2, 57 - 69, 01.07.2025

Fatih Hezenci , Hüseyin Budak

https://doi.org/10.33434/cams.1660607

Abstract

In this paper, some Euler-Maclaurin-type inequalities are established by using $h-$convex functions involving Riemann-Liouville fractional integrals. In precisely, using the properties of $h$-convex functions, we prove new Euler-Maclaurin-type inequalities. In addition, we present some Euler-Maclaurin-type inequalities for Riemann-Liouville fractional integrals by using Hölder inequality. Moreover, some Euler-Maclaurin-type inequalities are established by using power-mean inequality. Finally, by using the special choices of the obtained results, we obtain some Euler-Maclaurin-type inequalities.

Keywords

Convex functions , Fractional calculus , Maclaurin , Quadrature formula

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