Ostrowski Type Inequalities and Applications in Numerical Integration

Editors: Sever S. Dragomir, Themistocles M. Rassias



It was noted in the preface of the book "Inequalities Involving Functions and Their Integrals and Derivatives", Kluwer Academic Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink; since the writing of the classical book by Hardy, Littlewood and Polya (1934), the subject of differential and integral inequalities has grown by about 800%. Ten years on, we can confidently assert that this growth will increase even more significantly. Twenty pages of Chapter XV in the above mentioned book are devoted to integral inequalities involving functions with bounded derivatives, or, Ostrowski type inequalities. This is now itself a special domain of the Theory of Inequalities with many powerful results and a large number of applications in Numerical Integration, Probability Theory and Statistics, Information Theory and Integral Operator Theory. The main aim of the present book, jointly written by the members of the Vic- toria University node of RGMIA (Research Group in Mathematical Inequali- ties and Applications, http: I /rgmia. vu. edu. au) and Th. M. Rassias, is to present a selected number of results on Ostrowski type inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadrature for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given.

Table of contents

Front Matter
Pages i-xix

Generalisations of the Ostrowski Inequality and Applications
Pages 1-63

Integral Inequalities for N—Times Differentiable Mappings
Pages 65-139

Three Point Quadrature Rules
Pages 141-250

Product Branched Peano Kernels and Numerical Integration
Pages 251-284

Ostrowski Type Inequalities for Multiple Integrals
Pages 285-329

Some Results for Double Integrals Based on an Ostrowski Type Inequality
Pages 331-371

Product Inequalities and Weighted Quadrature
Pages 373-416

Some Inequalities for the Riemann-Stieltjes Integral
Pages 417-477

Back Matter
Pages 479-481