Refinements of Jensen’s and McShane’s inequalities with applications
Muhammad Adil Khan, Josip Pečarić, Yu‐Ming Chu
Abstract
In this article, we consider the generalized forms of the Jensen's inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen's and McShane's inequalities connected to certain functions from the linear space, generalize the Jessen's and McShane's inequalities pertaining n certain functions. As applications, we provide some improvements for the generalized means, Holder and generalized Beck's inequalities.
Topics & Concepts
MathematicsInequalityJensen's inequalityPure mathematicsCalculus (dental)Mathematical analysisGeometryMedicineConvex analysisRegular polygonConvex optimizationDentistryMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsMathematical functions and polynomials