Convex Functions, Partial Orderings, and Statistical Applications

Content: 
Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages xi-xii
J.E.P., F.P., Y.L.T.

Notation and Numbering System
Page xiii

Chapter 1 Convex Functions
Pages 1-42

Chapter 2 Jensen's and Jensen—Steffensen's Inequalities
Pages 43-82

Chapter 3 Reversals, Refinements, and Converses of Jensen's and Jensen—Steffensen's Inequalities
Pages 83-105

Chapter 4 Applications of Jensen's Inequality to Means and Hölder's Inequalities
Pages 107-135

Chapter 5 Hermite—Hadamard's and Jensen—Petrović's Inequalities
Pages 137-169

Chapter 6 Popoviciu's, Burkill's, and Steffensen's Inequalities
Pages 171-195

Chapter 7 Čebyšev—Grüss', Favard's, Berwald's, Gauss—Winckler's, and Related Inequalities
Pages 197-228

Chapter 8 Hardy's, Hilbert's, Opial's, Young's, Nanson's, and Related Inequalities
Pages 229-251

Chapter 9 General Linear Inequalities for Convex Sequences and Functions
Pages 253-276

Chapter 10 Orderings and Convexity-Preserving Transformations
Pages 277-305

Chapter 11 Convex Functions and Geometric Inequalities
Pages 307-317

Chapter 12 Convexity, Majorization, and Schur-Convexity
Pages 319-338

Chapter 13 Convexity and Log-Concavity Related Moment and Probability Inequalities
Pages 339-359

Chapter 14 Muirhead's Theorem and Related Inequalities
Pages 361-374

Chapter 15 Arrangement Ordering
Pages 375-389

Chapter 16 Applications of Arrangement Ordering
Pages 391-405

Chapter 17 Multivariate Arrangement Increasing Functions
Pages 407-418

References Review Article
Pages 419-456

Author Index
Pages 457-462

Subject Index
Pages 463-467