IMPROVEMENTS ON SOME INEQUALITIES OF HERMITE HADAMARD INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE SECOND DERIVATIVE h AND P-CONVEX - Unluyol, Erdal; Salas, Seren; Dalkun, Gorkem (TWMS journal of applied and engineering mathematics, 2021)
In this paper, firstly we obtain some improvements of Hermite-Hadamard integral inequalities via h and P-convex by using Holder-Iscan inequality. Secondly new results are established. Thirdly, we determine some new inequalities for functions when a power of the absolute value of second derivatives are h and P-convex. Finally they are compared with the old ones. Keywords:Holder-Iscan integral inequality, improved power-mean integral inequality, Hermite Hadamard integral inequality, h and P-convexity. AMS Subject Classification: 26A51, 26D10, 26D15