Jensen-type inequalities for <i>m</i>-convex functions
Paul Bosch, Yamilet Quintana, José M. Rodrı́guez, José M. Sigarreta
Abstract
Abstract Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays the 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 apply them to generalized Riemann-Liouville-type integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.
Topics & Concepts
MathematicsUniquenessConvex functionInequalityType (biology)Pure mathematicsRegular polygonJensen's inequalityYoung's inequalityMathematical analysisConvex analysisConvex optimizationRearrangement inequalityLog sum inequalityGeometryEcologyBiologyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsNonlinear Differential Equations Analysis