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