Inequalities of Hermite-Hadamard type for higher order convex functions, revisited
Tomasz Szostok
Abstract
In this paper we present a very short proof of inequalities of Hermite-Hadamard type obtained by M. Bessenyei and Zs. Páles. This proof is based on the recently developed method connected with use of stochastic orderings of random variables. In the second part of the paper we present a way to extend these known inequalities. Namely, we describe completely the possible inequalities of Hermite-Hadamard type for longer expression than it was the case in the results of Bessenyei and Páles.
Topics & Concepts
Hermite polynomialsMathematicsHadamard transformType (biology)Convex functionPure mathematicsInequalityOrder (exchange)Regular polygonMathematical analysisApplied mathematicsGeometryEconomicsBiologyEcologyFinanceMathematical Inequalities and ApplicationsMathematical functions and polynomials