On Ostrowski type inequalities via the Taylor's formula

In the present article, our aim is to obtain new Ostrwoski type inequalities by using Taylor's formula with weighted Montgomery identity and the Green's function. The results we acquire containing the identities for the sum \sum_{i=۱}^m p_i f_{۱}(\lambda_ i) and the integral \int^{\nu}_{\mu} p(\xi)  f_{۱}(g(\xi) )\, d\xi. We also estimate the difference of two weighted integral means for the result obtained by the Taylor formula with weighted Montgomery identity.

Keywords:

Ostrowski inequality , Taylor's formula , Green's function , Integral means