Convex Functions, Partial Orderings, and Statistical Applications

Josip E. Peajcariaac, Y. L. Tong

• Publisher: Academic Press
• Year: 1992
• Print ISBN: 9780125492508
• eBook ISBN: 9780080925226
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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. - 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

Table of contents

• Cover image
• Title page
• Table of Contents
• Inside Front Matter
• Front Matter
• Copyright page
• Dedication
• Preface
• Notation and Numbering System
• Chapter 1: Convex Functions
• Chapter 2: Jensen’s and Jensen–Steffensen’s Inequalities
• Chapter 3: Reversals, Refinements, and Converses of Jensen’s and Jensen–Steffensen’s Inequalities
• Chapter 4: Applications of Jensen’s Inequality to Means and Hölder’s Inequalities
• Chapter 5: Hermite–Hadamard’s and Jensen–Petrovi’s Inequalities
• Chapter 6: Popoviciu’s, Burkill’s, and Steffensen’s Inequalities
• Chapter 7: Čebyšev–Grüss’, Favard’s, Berwald’s, Gauss–Winckler’s, and Related Inequalities
• Chapter 8: Hardy’s, Hilbert’s, Opial’s, Young’s, Nanson’s, and Related Inequalities
• Chapter 9: General Linear Inequalities for Convex Sequences and Functions
• Chapter 10: Orderings and Convexity-Preserving Transformations
• Chapter 11: Convex Functions and Geometric Inequalities
• Chapter 12: Convexity, Majorization, and Schur-Convexity
• Chapter 13: Convexity and Log-Concavity Related Moment and Probability Inequalities
• Chapter 14: Muirhead’s Theorem and Related Inequalities
• Chapter 15: Arrangement Ordering
• Chapter 16: Applications of Arrangement Ordering
• Chapter 17: Multivariate Arrangement Increasing Functions
• References
• Author Index
• Subject Index
• Mathematics in Science and Engineering