Two-point Ostrowski and Ostrowski–Grüss type inequalities with applications

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.