Intended for researchers and graduate students working in the fields of integral inequalities, approximation theory, applied mathematics, probability theory and stochastics, and numerical analysis.
Author(s): Sever S. Dragomir, Themistocles M. Rassias
Edition: 1
Publisher: Springer
Year: 2002
Language: English
Pages: 412
Preface......Page 5
1.1. Introduction......Page 9
1.2. Generalisations for Functions of Bounded Variation......Page 11
1.3. Generalisations for Functions whose Derivatives are in L......Page 23
1.4. Generalisation for Functions whose Derivatives are in Lp......Page 36
1.5. Generalisations in Terms of L1-norm......Page 50
Bibliography......Page 59
2.1. Introduction......Page 63
2.2. Integral Identities......Page 64
2.3. Integral Inequalities......Page 72
2.4. The Convergence of a General Quadrature Formula......Page 79
2.5. Grüss Type Inequalities......Page 83
2.6. Some Particular Integral Inequalities......Page 88
2.7. Applications for Numerical Integration......Page 112
Bibliography......Page 126
3.1. Introduction......Page 129
3.2. Bounds Involving at most a First Derivative......Page 131
3.3. Bounds for n-Time Differentiable Functions......Page 194
Bibliography......Page 218
4.1. Introduction......Page 223
4.2. Fundamental Results......Page 225
4.3. Simpson Type Formulae......Page 232
4.4. Perturbed Results......Page 234
4.5. More Perturbed Results Using -Seminorms......Page 243
Bibliography......Page 249
5.1. Introduction......Page 253
5.2. An Ostrowski Type Inequality for Double Integrals......Page 257
5.3. Other Ostrowski Type Inequalities......Page 271
5.4. Ostrowski's Inequality for Hölder Type Functions......Page 281
Bibliography......Page 288
6.1. Introduction......Page 291
6.3. Mapping Whose First Derivatives Belong to L(a,b)......Page 292
6.4. Numerical Results......Page 297
6.5. Application For Cubature Formulae......Page 298
6.6. Mapping Whose First Derivatives Belong to Lp(a,b).......Page 301
6.7. Application For Cubature Formulae......Page 304
6.8. Mappings Whose First Derivatives Belong to L1(a,b).......Page 306
6.9. Integral Identities......Page 309
6.10. Some Integral Inequalities......Page 313
6.11. Applications to Numerical Integration......Page 320
Bibliography......Page 322
7.1. Introduction......Page 325
7.2. Weight Functions......Page 326
7.3. Weighted Interior Point Integral Inequalities......Page 327
7.4. Weighted Boundary Point (Lobatto) Integral Inequalities......Page 340
7.5. Weighted Three Point Integral Inequalities......Page 347
Bibliography......Page 358
8.1. Introduction......Page 361
8.2. Some Trapezoid Like Inequalities for Riemann-Stieltjes Integral......Page 363
8.3. Inequalities of Ostrowski Type for the Riemann-Stieltjes Integral......Page 380
8.4. Some Inequalities of Grüss Type for Riemann-Stieltjes Integral......Page 400
Bibliography......Page 406
