Ostrowski and Landau inequalities for Banach space valued functions

Abstract

Very general univariate Ostrowski type inequalities are presented regarding Banach space valued functions. They provide norm estimates for the deviation of the average of the function from its vector values, and they involve the n th order vector derivative, n ≥ 1 , with respect to ‖ ⋅ ‖ p , 1 ≤ p ≤ ∞ . On the way to prove our results we establish useful functional vector identities. Using our vector Ostrowski inequalities we derive the vector Landau inequalities.