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-Ìsçan integral inequalities with the help of an identity. Then, the authors compare the results obtained with both Hölder-Ìsçan integral inequalities and prove that the Hölder-Ìsçan integral inequality gives a better approximation than the Hölder integral inequality. Also, some applications to special means of real numbers are also given.