New inequalities for $\eta$-quasiconvex functions

TL;DR

This paper develops new Ostrowski-type inequalities for $\

Contribution

It introduces novel inequalities for $\

Findings

Derived inequalities relate various means.

Established bounds for $\

Connected $\

Abstract

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.