Ostrowski and Landau inequalities for Banach space valued functions
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 nth order vector derivative, n >= 1, with respect to parallel to.parallel to, 1 <= p <= infinity. On the way to prove our results we establish useful functional vector identities. Using our vector Ostrowski inequalities we derive the vector Landau inequalities. (C) 2011 Elsevier Ltd. All rights reserved
landau inequality ostrowski inequality univariate integral inequality montgomery identity vector valued functions