Convex Functions, Partial Orderings, and Statistical Applications

Josip E. Pečarić, Frank Proschan and Y.L. Tong (Eds.)0125492502, 9780125492508, 9780080925226

This research-level book presents up-to-date information concerning recent developments in convex functions and partial orderings and some applications in mathematics, statistics, and reliability theory. The book will serve researchers in mathematical and statistical theory and theoretical and applied reliabilists. Key Features * Presents classical and newly published results on convex functions and related inequalities * Explains partial ordering based on arrangement and their applications in mathematics, probability, statsitics, and reliability * Demonstrates the connection of partial ordering with other well-known orderings such as majorization and Schur functions * Will generate further research and applications

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Table of contents :
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