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.

This book is the first in a collection of research monographs that are devoted to presenting recent research, development and use of Mathematical Inequalities for Special Functions. All the papers incorporated in the book have peen peer-reviewed and cover a range of topics that include both survey material of previously published works as well as new results. In his presentation on special functions approximations and bounds via integral representation, Pietro Cerone utilises the classical Stevensen inequality and bounds for the  Ceby sev functional to obtain bounds for some classical special functions. The methodology relies on determining bounds on integrals of products of functions. The techniques are used to obtain novel and useful bounds for the Bessel function of the first kind, the Beta function, the Zeta function and Mathieu series.

The main aim of the present work is to present a number of selected results on Ostrowski-type integral inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadratures for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given. Topics dealt with include generalisations of the Ostrowski inequality and its applications; integral inequalities for n-times differentiable mappings; three-point quadrature rules; product-branched Peano kernels and numerical integration; Ostrowski-type inequalities for multiple integrals; results for double integrals based on an Ostrowski-type inequality; product inequalities and weighted quadrature; and some inequalities for the Riemann-Stieltjes integral.

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.

This book is the first in a collection of research monographs that are devoted to presenting recent research, development and use of Mathematical Inequalities for Special Functions. All the papers incorporated in the book have peen peer-reviewed and cover a range of topics that include both survey material of previously published works as well as new results. In his presentation on special functions approximations and bounds via integral representation, Pietro Cerone utilises the classical Stevensen inequality and bounds for the  Ceby sev functional to obtain bounds for some classical special functions. The methodology relies on determining bounds on integrals of products of functions. The techniques are used to obtain novel and useful bounds for the Bessel function of the first kind, the Beta function, the Zeta function and Mathieu series.

The main aim of the present work is to present a number of selected results on Ostrowski-type integral inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadratures for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given. Topics dealt with include generalisations of the Ostrowski inequality and its applications; integral inequalities for n-times differentiable mappings; three-point quadrature rules; product-branched Peano kernels and numerical integration; Ostrowski-type inequalities for multiple integrals; results for double integrals based on an Ostrowski-type inequality; product inequalities and weighted quadrature; and some inequalities for the Riemann-Stieltjes integral.