Jensen-type inequalities for convex and $m$-convex functions via fractional calculus

Yamilet Quintana, José M. Rodríguez, José M. Sigarreta Almira

Published 2022-01-21Version 1

In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work we prove some new Jensen-type inequalities for $m$-convex functions, and we apply them to generalized Riemann-Liouville-type integral operators. It is remarkable that, if we consider $m=1$, we obtain new inequalities for convex functions.