Petrović-Type Inequalities for Harmonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>h</mml:mi></mml:math>-convex Functions
Imran Abbas Baloch, Yu‐Ming Chu
Abstract
In the article, we establish several Petrović-type inequalities for the harmonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>h</mml:mi></mml:math>-convex (concave) function if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>h</mml:mi></mml:math> is a submultiplicative (super-multiplicative) function, provide some new majorizaton type inequalities for harmonic convex function, and prove the superadditivity, subadditivity, linearity, and monotonicity properties for the functionals derived from the Petrović type inequalities.
Topics & Concepts
SubadditivityHarmonic meanMonotonic functionType (biology)MathematicsConvex functionMultiplicative functionAlgorithmFunction (biology)Regular polygonHarmonic functionLogarithmically convex functionApplied mathematicsConvex optimizationConvex combinationCombinatoricsMathematical analysisStatisticsGeometryEvolutionary biologyEcologyBiologyMathematical Inequalities and ApplicationsAnalytic and geometric function theoryFunctional Equations Stability Results