Contents -- Preface -- 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 -- Bibliography -- List of Symbols -- Index.