Selected Topics on Hermite-Hadamard Inequalities and Applications

1. Preface......Page 5
1. Historical Considerations......Page 7
2. Characterisations of Convexity via H-H Inequalities......Page 9
3. Some Generalisations......Page 11
1. Generalisations of the H-H Inequality......Page 15
2. Hadamard's Inferior and Superior Sums......Page 25
3. A Refinement of the H-H Inequality for Modulus......Page 31
4. Further Inequalities for Differentiable Convex Functions......Page 35
5. Further Inequalities for Twice Differentiable Convex Functions......Page 44
6. A Best Possible H-H Inequality in Fink's Sense......Page 59
7. Generalised Weighted Mean Values of Convex Functions......Page 65
8. Generalisations for n-Time Differentiable Functions......Page 70
9. The Euler Formulae and Convex functions......Page 75
10. H-H Inequality for Isotonic Linear Functionals......Page 83
11. H-H Inequality for Isotonic Sublinear Functionals......Page 90
1. Two Difference Mappings......Page 97
2. Properties of Superadditivity and Supermultiplicity......Page 104
3. Properties of Some Mappings Defined By Integrals......Page 111
4. Some Results due to B.G. Pachpatte......Page 132
5. Fejér's Generalization of the H-H Inequality......Page 135
6. Further Results Refining the H-H Inequality......Page 144
7. Another Generalisation of Féjer's Result......Page 153
1. Some Sequences Defined by Multiple Integrals......Page 159
2. Convergence Results......Page 165
3. Estimation of Some Sequences of Multiple Integrals......Page 170
4. Further Generalizations......Page 180
5. Properties of the Sequence of Mappings Hn......Page 184
6. Applications for Special Means......Page 201
1. Integral Inequalities of H-H Type for Log-Convex Functions......Page 203
2. The H-H Inequality for r-Convex Functions......Page 211
3. Stolarsky Means and H-H's Inequality......Page 217
4. Functional Stolarsky Means and H-H Inequality......Page 223
5. Generalization of H-H Inequality for G-Convex Functions......Page 232
6. H-H Inequality for the Godnova-Levin Class of Functions......Page 242
7. The H-H Inequality for Quasi-Convex Functions......Page 250
8. P-functions, Quasiconvex Functions and H-H Type Inequalities......Page 256
9. Convexity According to the Geometric Mean......Page 264
10. The H-H Inequality of s-Convex Functions in the First Sense......Page 282
11. The Case for s-Convex Functions in the Second Sense......Page 292
12. Inequalities for m-Convex and ( 0=x"010B,m) -Convex Functions......Page 299
13. Inequalities for Convex-Dominated Functions......Page 306
14. H-H Inequality for Lipschitzian Mappings......Page 313
1. An Inequality for Convex Functions on the Co-ordinates......Page 321
2. A H-H Inequality on the Disk......Page 329
3. A H-H Inequality on a Ball......Page 338
4. A H-H Inequality for Functions on a Convex Domain......Page 345
Bibliography......Page 348