New refinement of the Jensen inequality associated to certain functions with applications
Muhammad Adil Khan, Đilda Pečarić, Josip Pečarić
Abstract
Abstract This article proposes a new refinement of the celebrated Jensen inequality. Some refinements have been obtained for quasi-arithmetic means, Hölder and Hermite–Hadamard inequalities. Several applications are given in information theory. A more general refinement of Jensen inequality is presented associated to n functions.
Topics & Concepts
MathematicsJensen's inequalityInequalityLog sum inequalityKantorovich inequalityInequality of arithmetic and geometric meansHadamard transformAlgebra over a fieldRearrangement inequalityHölder's inequalityPure mathematicsHermite polynomialsYoung's inequalityKy Fan inequalityCalculus (dental)Mathematical analysisLinear inequalityRegular polygonConvex analysisGeometryConvex optimizationDentistryMedicineMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsMathematical functions and polynomials