New inequalities for $\eta$-quasiconvex functions

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 $q\ge 1$, 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.

This is a preprint of a paper whose final and definite form is accepted 19-Sept-2018 as a book chapter at Springer New York, on the topic of 'Frontiers in Functional Equations and Analytic Inequalities', Edited by G. Anastassiou and J. Rassias