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.
Author(s): Sever S. Dragomir, Themistocles Rassias
Edition: 2002
Publisher: Springer
Year: 2002
Language: English
Commentary: Better bookmarks, page cut, pagination.
Pages: 412
Ostrowski Type Inequalities and Applications in Numerical Integration
Contents
Generalisations of Ostrowski Inequality and Applications
1.1. Introduction
1.2. Generalisations for Functions of Bounded Variation
1.3. Generalisations for Functions whose Derivatives are in L
1.4. Generalisation for Functions whose Derivatives are in Lp
1.5. Generalisations in Terms of L1 norm
Bibliography
Integral Inequalities for n Times Differentiable Mappings
2.1. Introduction
2.2. Integral Identities
2.3. Integral Inequalities
2.4. The Convergence of a General Quadrature Formula
2.5. Gruss Type Inequalities
2.6. Some Particular Integral Inequalities
2.7. Applications for Numerical Integration
2.8. Concluding Remarks
Bibliography
Three Point Quadrature Rules
3.1. Introduction
3.2. Bounds Involving at most a First Derivative
3.2.3. A Generalized Ostrowski-Grss Inequality Using Cauchy-Schwartz.
3.2.4. A Generalized Ostrowski-Gruss Inequality Via a New Identity.
3.2.6. Grss-type Inequalities for Functions whose First Derivative
3.2.8. Grss-type Inequalities for Functions whose First Derivative
3.2.9. Three Point Inequalities for Mappings of Bounded Variation,
3.3. Bounds for n Time Differentiable Functions
Bibliography
Product Branches of Peano Kernels and Numerical Integration
4.1. Introduction
4.2. Fundamental Results
4.3. Simpson Type Formulae
4.4. Perturbed Results
4.5. More Perturbed Results Using Seminorms
4.6. Concluding Remarks
Bibliography
Ostrowski Type Inequalities for Multiple Integrals
5.1. Introduction
5.2. An Ostrowski Type Inequality for Double Integrals
5.3. Other Ostrowski Type Inequalities
5.4. Ostrowski's Inequality for Hlder Type Functions
Bibliography
Some Results for Double Integrals Based on an Ostrowski Type Inequality
6.1. Introduction
6.2. The One Dimensional Ostrowski Inequality
6.3. Mapping Whose First Derivatives Belong to L (a, b)
6.4. Numerical Results
6.5. Application For Cubature Formulae
6.6. Mapping Whose First Derivatives Belong to Lp(a, b).
6.7. Application For Cubature Formulae
6.8. Mappings Whose First Derivatives Belong to L1(a, b).
6.9. Integral Identities
6.10. Some Integral Inequalities
6.11. Applications to Numerical Integration
Bibliography
Product Inequalities and Weighted Quadrature
7.1. Introduction
7.2. Weight Functions
7.3. Weighted Interior Point Integral Inequalities
7.4. Weighted Boundary Point (Lobatto) Integral Inequalities
7.4.1. Development of a Product-Trapezoidal Like Quadrature Rule.
7.5. Weighted Three Point Integral Inequalities
Bibliography
Some Inequalities for Riemann-Stieltjes Integral
8.1. Introduction
8.2. Some Trapezoid Like Inequalities for Riemann-Stieltjes Integral
8.3. Inequalities of Ostrowski Type for the Riemann-Stieltjes Integral
8.3.4. Another Inequality of Ostrowski Type for the Riemann-Stieltjes
8.4. Some Inequalities of Grss Type for Riemann-Stieltjes Integral
8.4.3. A Numerical Quadrature Formula for the Riemann-Stieltjes
8.4.4. Quadrature Methods for the Riemann-Stieltjes Integral of Con-
Bibliography
