Mathematical inequalities [1st ed] 0444517952, 9780444517951, 9780080459394

Table of contents :
front cover......Page 1
copyright......Page 6
Preface......Page 9
table of contents......Page 11
Introduction......Page 15
1.2 Jensen’s and Related Inequalities......Page 25
1.3 Jessen’s and Related Inequalities......Page 47
1.4 Some General Inequalities Involving Convex Functions......Page 60
1.5 Hadamard’s Inequalities......Page 67
1.6 Inequalities of Hadamard Type I......Page 78
1.7 Inequalities of Hadamard Type II......Page 87
1.8 Some Inequalities Involving Concave Functions......Page 98
1.9 Miscellaneous Inequalities......Page 114
1.10 Notes......Page 125
2.2 Hardy’s Series Inequality and Its Generalizations......Page 127
2.3 Series Inequalities Related to Those of Hardy, Copson and Littlewood......Page 142
2.4 Hardy’s Integral Inequality and Its Generalizations......Page 158
2.5 Further Generalizations of Hardy’s Integral Inequality......Page 169
2.6 Hardy-Type Integral Inequalities......Page 183
2.7 Multidimensional Hardy-Type Inequalities......Page 198
2.8 Inequalities Similar to Hilbert’s Inequality......Page 223
2.9 Miscellaneous Inequalities......Page 253
2.10 Notes......Page 274
3.2 Opial-Type Integral Inequalities......Page 277
3.3 Wirtinger–Opial-Type Integral Inequalities......Page 289
3.4 Inequalities Related to Opial’s Inequality......Page 304
3.5 General Opial-Type Integral Inequalities......Page 312
3.6 Opial-Type Inequalities Involving Higher-Order Derivatives......Page 322
3.7 Opial-Type Inequalities in Two and Many Independent Variables......Page 342
3.8 Discrete Opial-Type Inequalities......Page 363
3.9 Miscellaneous Inequalities......Page 377
3.10 Notes......Page 393
4.1 Introduction......Page 395
4.2 Inequalities of Poincaré, Sobolev and Others......Page 396
4.3 Poincaré- and Sobolev-Type Inequalities I......Page 405
4.4 Poincaré- and Sobolev-Type Inequalities II......Page 416
4.5 Inequalities of Dubinskii and Others......Page 433
4.6 Poincaré- and Sobolev-Like Inequalities......Page 444
4.7 Some Extensions of Rellich’s Inequality......Page 459
4.8 Poincaré- and Sobolev-Type Discrete Inequalities......Page 471
4.9 Miscellaneous Inequalities......Page 482
4.10 Notes......Page 496
5.2 Inequalities of Levin and Others......Page 499
5.3 Levin-Type Inequalities......Page 509
5.4 Inequalities Related to Lyapunov’s Inequality......Page 519
5.5 Extensions of Lyapunov’s Inequality......Page 530
5.6 Lyapunov-Type Inequalities I......Page 539
5.7 Lyapunov-Type Inequalities II......Page 548
5.8 Lyapunov-Type Inequalities III......Page 556
5.9 Miscellaneous Inequalities......Page 567
5.10 Notes......Page 576
References......Page 579
Index......Page 603