Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings
Xuexiao You, Muhammad Aamir Ali, Hüseyin Budak, Jiraporn Reunsumrit, Thanin Sitthiwirattham
Abstract
In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions. We also prove Hermite–Hadamard–Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities.
Topics & Concepts
Hadamard transformHermite polynomialsMathematicsConvex functionType (biology)Pure mathematicsInequalityRegular polygonAlgebra over a fieldMathematical analysisGeometryEcologyBiologyMathematical Inequalities and ApplicationsMathematical functions and polynomialsFunctional Equations Stability Results