| List of Figures |
| List of Tables |
| Preface |
| Symbols List |
| Generalisations of the Ostrowski Inequality and Applications / Sever S. Dragomir ; Themistocles M. Rassias1： |
| Introduction |
| Generalisations for Functions of Bounded Variation / 2： |
| Some Inequalities / 2.1： |
| A General Quadrature Formula / 2.2： |
| Particular Inequalities / 2.3： |
| Particular Quadrature Formulae / 2.4： |
| Generalisations for Functions whose Derivatives are in L[subscript infinity] / 3： |
| Generalisation for Functions whose Derivatives are in L[subscript p] / 3.1： |
| General Quadrature Formulae / 4.1： |
| Generalisations in Terms of L[subscript 1]-norm / 4.3： |
| Integral Inequalities for n-Times Differentiable Mappings / Anthony Sofo5.1： |
| Integral Identities |
| Integral Inequalities |
| The Convergence of a General Quadrature Formula |
| Gruss Type Inequalities |
| Some Particular Integral Inequalities / 6： |
| Applications for Numerical Integration / 7： |
| Concluding Remarks / 8： |
| Three Point Quadrature Rules / Pietro Cerone |
| Bounds Involving at most a First Derivative |
| Inequalities Involving the First Derivative |
| Application in Numerical Integration |
| A Generalized Ostrowski-Gruss Inequality Using Cauchy-Schwartz |
| A Generalized Ostrowski Gruss Inequality Via a New Identity |
| Inequalities for which the First Derivative Belongs to L[subscript 1] [a, b] / 2.5： |
| Gruss-type Inequalities for Functions whose First Derivative Belongs to L[subscript 1] [a, b] / 2.6： |
| Inequalities for which the First Derivative Belongs to L[subscript p] [a, b] / 2.7： |
| Gruss-type Inequalities for Functions whose First Derivative Belongs to L[subscript p] [a, b] / 2.8： |
| Three Point Inequalities for Mappings of Bounded Variation, Lipschitzian or Monotonic / 2.9： |
| Conclusion and Discussion / 2.10： |
| Bounds for n--Time Differentiable Functions |
| Some Integral Identities |
| Perturbed Rules Through Gruss Type Inequalities |
| Perturbed Rules From Premature Inequalities / 3.5： |
| Applications in Numerical Integration / 3.6： |
| Product Branched Peano Kernels and Numerical Integration / 3.7： |
| Fundamental Results |
| Simpson Type Formulae |
| Perturbed Results |
| More Perturbed Results Using [Delta] - Seminorms |
| Ostrowski Type Inequalities for Multiple Integrals / Neil S. Barnett |
| An Ostrowski Type Inequality for Double Integrals |
| Some Inequalities in Terms of [double vertical line] . [double vertical line subscript infinity]--Norm |
| Applications for Cubature Formulae |
| Some Inequalities in Terms of [double vertical line] . [double vertical line subscript p]--Norm |
| Applications For Cubature Formulae |
| Some Inequalities in Terms of [double vertical line] . [double vertical line subscript 1]--Norm |
| Other Ostrowski Type Inequalities |
| Some Identities |
| Some Bounds |
| Ostrowski's Inequality for Holder Type Functions |
| The Unweighted Case |
| The Weighted Case |
| Results for Double Integrals Based on an Ostrowski Type Inequality / George Hanna |
| Techniques for Two Dimensional Integrals |
| Mappings Whose First Derivative Belongs to L[subscript infinity a, b] / 1.1： |
| Application to Cubature Formulae / 1.3： |
| Mappings Whose First Derivative Belongs to L[subscript p a, b] / 1.4： |
| Mappings Whose First Derivative Belongs to L[subscript 1](a, b) / 1.5： |
| Numerical Results / 1.7： |
| A General Ostrowski Type Inequality for Double Integrals |
| Some Integral Inequalities |
| Applications to Numerical Integration |
| Product Inequalities and Weighted Quadrature / John Roumeliotis |
| Weight Functions |
| Interior Point Inequalities |
| Two Interior Points |
| Some Weighted Integral Inequalities |
| Uniform (Legendre) / 3.2.1： |
| Logarithm / 3.2.2： |
| Jacobi / 3.2.3： |
| Chebyshev / 3.2.4： |
| Laguerre / 3.2.5： |
| Hermite / 3.2.6： |
| Weighted Boundary Point (Lobatto) Integral Inequalities |
| Development of a Product-Trapezoidal Like Quadrature Rule |
| Numerical Experiment |
| Some Particular Weighted Integral Inequalities |
| Weighted Three Point Integral Inequalities / 4.3.1： |
| Development of a Quadrature Rule |
| Application of Gruss Type Inequalities / 5.1.1： |
| Gruss-type Inequalities for Some Weight Functions |
| Legendre / 5.3.1： |
| Some Inequalities for the Riemann-Stieltjes Integral / 5.3.2： |
| Some Trapezoid Like Inequalities for Riemann-Stieltjes Integral |
| A Trapezoid Formula for the Riemann-Stieltjes Integral |
| Approximation of the Riemann-Stieltjes Integral |
| Another Trapezoid Like Inequality |
| A Generalisation of the Trapezoid Inequality |
| Approximating the Riemann-Stieltjes Integral |
| Inequalities of Ostrowski Type for the Riemann-Stieltjes Integral |
| Another Inequality of Ostrowski Type for the Riemann-Stieltjes Integral |
| Some Inequalities of Gruss Type for the Riemann-Stieltjes Integral |
| A Numerical Quadrature Formula for the Riemann-Stieltjes Integral |
| Quadrature Methods for the Riemann-Stieltjes Integral of Continuous Mappings |
| Index |
| List of Figures |
| List of Tables |
| Preface |
| Symbols List |
| Generalisations of the Ostrowski Inequality and Applications / Sever S. Dragomir ; Themistocles M. Rassias1： |
| Introduction |
