Description

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

@introbul:Key Features @bul:* 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

Readership

Research-level mathematicians, statisticians, and engineers, as well as second-year graduate students in these areas.

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.

Details

No. of pages:
467
Language:
English
Copyright:
© 1992
Published:
Imprint:
Academic Press
Electronic ISBN:
9780080925226
Print ISBN:
9780125492508

About the authors