Semi P-geometric-arithmetically functions and some new related inequalities

Abstract

In this manuscript, the authors introduce the concept of the semi P-geometric-arithmetically functions (semi P-GA functions) and give their some algebraic properties. Then, they get Hermite-Hadamard's integral inequalities for semi P-GA-functions (geometric-arithmetically convex). In addition, the authors obtain new inequalities by using Hölder and Hölder-İşcan integral inequalities with the help of an identity. Then, the aouthors compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the Hölder-İşcan integral inequality gives a better approximation than the Hölder integral inequality. Also, some applications to special means of real numbers are also given.