Some inequalities for the s-Godunova–Levin type functions

In this paper, first, we obtained two new s-Godunova–Levin type inequalities about “the mean value Theorem for integrals”. Second, some inequalities were proved for mappings qth powers of first derivatives belonging to class Qs(I) using the Čebyšev’s inequality, H ölder inequality, Power mean inequality, and some other classical inequalities. Finally, some error estimates for the Trapezoidal formula are also given.The results obtained are consistent with literature.