  The class of $\eta$-quasiconvex functions was introduced in 2016. Here we
establish novel inequalities of Ostrowski type for functions whose second
derivative, in absolute value raised to the power $q\geq 1$, is
$\eta$-quasiconvex. Several interesting inequalities are deduced as special
cases. Furthermore, we apply our results to the arithmetic, geometric,
Harmonic, logarithmic, generalized log and identric means, getting new
relations amongst them.
