Jensen-type inequalities for convex and \(m\)-convex functions via fractional calculus

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 s...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Quintana, Yamilet, Rodríguez, José M, José M Sigarreta Almira
Format: Article
Language:English
Subjects:
Applications of mathematics
Boundary value problems
Convex analysis
Differential equations
Fractional calculus
Inequalities
Mathematical analysis
Operators (mathematics)
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 \(m\)-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.
ISSN:2331-8422