Jensen-type inequalities for convex and $m$-convex functions via fractional calculus
Classical Analysis and ODEs
2022-02-09 v2
Abstract
Inequalities play an important role in pure and applied mathematics. 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 -convex functions, and we apply them to generalized Riemann-Liouville-type integral operators. It is remarkable that, if we consider , we obtain new inequalities for convex functions.
Keywords
Cite
@article{arxiv.2202.03145,
title = {Jensen-type inequalities for convex and $m$-convex functions via fractional calculus},
author = {Yamilet Quintana and José M. Rodríguez and José M. Sigarreta Almira},
journal= {arXiv preprint arXiv:2202.03145},
year = {2022}
}