Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
Miguel José Vivas Cortez, Muhammad Aamir Ali, Hüseyin Budak, Humaira Kalsoom, Praveen Agarwal
Abstract
In this investigation, for convex functions, some new (p,q)-Hermite-Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)π2 integral are offered. It is also shown that the newly proved results for p=1 and q→1- can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.
Topics & Concepts
Hadamard transformMathematicsConvex functionMidpointHermite polynomialsDifferentiable functionPure mathematicsType (biology)Regular polygonInequalityYoung's inequalityMathematical analysisRearrangement inequalityLog sum inequalityGeometryEcologyBiologyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsMathematical functions and polynomials