Convex Functions, Partial Orderings, and Statistical Applications

by Josip E. Peajcariaac, Y. L. Tong

Overview

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.

Product Details

ISBN-13:	9780125492508
Publisher:	Elsevier Science
Publication date:	04/28/1992
Series:	Mathematics in Science and Engineering Series , #18
Pages:	467
Product dimensions:	5.94(w) x 9.00(h) x (d)

Table of Contents

Convex Functions. Jensen's and Jensen-Steffensen's Inequalities. Reversals, Refinements, and Converses of Jensen's and Jensen-Steffensen's Inequalities. Applications of Jensen's Inequality to Means and H*adolder's Inequalities. Hermite-Hadamard's and Jensen-Petrovi*aac's Inequalities. Popoviciu's, Burkill's, and Steffensen's Inequalities. *ajCeby*ajsev-Gr*aduss', Favard's, Berwald's, Gauss-Winckler's, and Related Inequalities. Hardy's, Hilbert's, Opial's, Young's, Nanson's, and Related Inequalities. General Linear Inequalities for Convex Sequences and Functions. Orderings and Convexity-Preserving Transformations. Convex Functions and Geometric Inequalities. Convexity, Majorization, and Schur-Convexity. Convexity and Log-Concavity Related Moment and Probability Inequalities. Muirhead's Theorem and Related Inequalities. Arrangement Ordering. Applications of Arrangement Ordering. Multivariate Arrangement Increasing Functions. References. Author Index. Subject Index.

Editorial Reviews

An advanced and comprehensive treatment of convex functions, along with some related partial orderings and selected applications in probability and statistics. Emphasizes the special role played by inequalities in the theory, noting that the definition of the class of convex functions is itself an inequality. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews