English

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 mm-convex functions, and we apply them to generalized Riemann-Liouville-type integral operators. It is remarkable that, if we consider m=1m=1, 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}
}