# Two-point Ostrowski and Ostrowski-Gr\"uss type inequalities with applications

## TL;DR

This paper extends two-point Ostrowski and Ostrowski-Grüss inequalities for n-times differentiable functions, providing new formulas, identities, error estimates, and generalizations with applications in approximation theory.

## Contribution

It introduces a generalized two-point Ostrowski formula, a Fink type identity, and extends these results to harmonic polynomial sequences, with new bounds and error estimates.

## Key findings

- Derived extended two-point Ostrowski formulas
- Established new Ostrowski-Grüss inequalities
- Provided error bounds and generalizations for polynomial sequences

## Abstract

In this work, an extension of two-point Ostrowski's formula for $n$-times differentiable functions is proved. A generalization of Taylor formula is deduced. An identity of Fink type for this extension is provided. Error estimates for the considered formulas are also given. Two-point Ostrowski-Gruss type inequalities are pointed out. An expansion of Guessab--Schmeisser two points formula for $n$-times differentiable functions via Fink type identity is established. Generalization of the main result for harmonic sequence of polynomials is established. Several bounds of the presented results are proved.