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Advanced Inequalities /
This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2011.
|
| Colección: | Series on concrete and applicable mathematics ;
v. 11. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Introduction
- 2. Advanced univariate Ostrowski type inequalities. 2.1. Introduction. 2.2. Auxilliary results. 2.3. Main results
- 3. Higher order Ostrowski inequalities. 3.1. Introduction. 3.2. Main results
- 4. Multidimensional Euler identity and optimal multidimensional Ostrowski inequalities. 4.1. Introduction. 4.2. Background. 4.3. Main results. 4.4. Applications. 4.5. Sharpness
- 5. More on multidimensional Ostrowski type inequalities. 5.1. Introduction. 5.2. Auxilliary results. 5.3. Main results
- 6. Ostrowski inequalities on Euclidean domains. 6.1. Introduction. 6.2. Main results
- 7. High order Ostrowski inequalities on Euclidean domains. 7.1. Introduction. 7.2. Main results. 7.3. Functions on general domains
- 8. Ostrowski inequalities on spherical shells. 8.1. Introduction. 8.2. Main results. 8.3. Addendum
- 9. Ostrowski inequalities on balls and shells via Taylor-Widder formula. 9.1. Introduction. 9.2. Background. 9.3. Results on the shell. 9.4. Results on the sphere. 9.5. Addendum
- 10. Multivariate opial type inequalities for functions vanishing at an interior point. 10.1. Introduction. 10.2. Main results
- 11. General multivariate weighted opial inequalities. 11.1. Introduction. 11.2. Main results
- 12. Opial inequalities for Widder derivatives. 12.1. Introduction. 12.2. Background. 12.3. Results
- 13. Opial inequalities for linear differential operators. 13.1. Background. 13.2. Results
- 14. Opial inequalities for vector valued functions. 14.1. Introduction. 14.2. Background. 14.3. Results. 14.4. Applications
- 15. Opial inequalities for semigroups. 15.1. Introduction. 15.2. Background. 15.3. Results
- 16. Opial inequalities for cosine and sine operator functions. 16.1. Introduction. 16.2. Background. 16.3. Results. 16.4. Applications.
- 17. Poincare like inequalities for linear differential operators. 17.1. Background. 17.2. Results
- 18. Poincare and Sobolev like inequalities for Widder derivatives. 18.1. Background. 18.2. Results
- 19. Poincare and Sobolev like inequalities for vector valued functions. 19.1. Introduction. 19.2. Background. 19.3. Results. 19.4. Applications
- 20. Poincare type inequalities for semigroups, cosine and sine operator functions. 20.1. Introduction. 20.2. Semigroups background. 20.3. Poincare type inequalities for semigroups. 20.4. Cosine and sine operator functions background. 20.5. Poincare type inequalities for cosine and sine operator functions
- 21. Hardy-Opial type inequalities. 21.1. Results
- 22. A basic sharp integral inequality. 22.1. Introduction. 22.2. Results
- 23. Estimates of the remainder in Taylor's formula. 23.1. Introduction. 23.2. Some new bounds for the remainder. 23.3. Some further bounds of the remainder. 23.4. Some inequalities for special cases. 23.5. Taylor-multivariate case estimates
- 24. The distributional Taylor formula. 24.1. Introduction and background. 24.2. Main results. 24.3. Applications
- 25. Chebyshev-Gruss type inequalities using Euler type and fink identities. 25.1. Background. 25.2. Main results
- 26. Gruss type multivariate integral inequalities. 26.1. Introduction. 26.2. Auxiliary result. 26.3. Main results
- 27. Chebyshev-Gruss type inequalities on spherical shells and balls. 27.1. Introduction. 27.2. Main results
- 28. Multivariate Chebyshev-Gruss and comparison of integral means inequalities. 28.1. Background. 28.2. Main results
- 29. Multivariate fink type identity applied to multivariate inequalities. 29.1. Introduction. 29.2. Main results. 29.3. Applications.