Ostrowski type inequalities on H-type groups

The main aim of this paper is to establish an Ostrowski type inequality on H-type groups using the L^∞ norm of the horizontal gradient. The work has been motivated by the work of Anastassiou and Goldstein in [G.A. Anastassiou, J.A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl. 337 (2008) 962-968].     

Higher order Ostrowski type inequalities over Euclidean domains

The classical Ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms of the maximum of its first derivative. This result is extended to functions on general domains using the L^∞ norm of its nth partial derivatives. For radial functions on balls the inequality is sharp.     

A Generalization of Ostrowski Integral Inequality for Mappings Whose Derivatives Belong to L_1 [a,b] and Applications in Numerical Integration

A generalization of Ostrowski integral inequality for mappings whose derivatives belong to L_1 [a,b], and applications for general quadrature formulae are given.     

有界变差函数的加权Ostrowski型不等式的改进及其应用(英文)

本文改进了有界变差函数的加权Ostrowski型不等式,并给出了其在求积公式中的应用.     

On Anastassiou's Generalizations of the Ostrowski Inequality and Related Results

We provide a generalization of a recent result of Anastassiou related to thewell-known Ostrowski inequality, as well as some related results. Ourresults subsume, extend, and consolidate a number of known results.     

Multivariate inequalities based on Sobolev representations

Here we derive very general multivariate tight integral inequalities of Chebyshev–Grüss, Ostrowski types and of comparison of integral means. These are based on well-known Sobolev integral representation of a function. Our inequalities engage ordinary and weak partial derivatives of the involved functions. We also give their applications. On the way to prove our main results we derive important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. Our results expand to all possible directions.     

Another generalization of weighted Ostrowski type inequality for mappings of bounded variation

A new generalization of weighted Ostrowski type inequality for mappings of bounded variation with a unified sharp bound is established.     

On Generalizations of Ostrowski Inequality and Some Related Results

Some generalizations of the Ostrowski inequality, the Milovanovi-Peari-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.     

Some Further Generalizations of Ostrowski Inequality for Hölder Functions and Functions with Bounded Derivatives

Some generalizations of Ostrowski inequality for Hölder functions and functions with bounded derivatives are given.