UID:
almafu_9958106769802883
Umfang:
1 online resource (485 p.)
ISBN:
1-282-03472-3
,
9786612034725
,
0-08-092522-7
Serie:
Mathematics in science and engineering ; v. 187
Inhalt:
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 o
Anmerkung:
Description based upon print version of record.
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Front Cover; Convex Functions, Partial Orderings, and Statistical Applications; Copyright Page; Contents; Preface; Notation and Numbering System; Chapter 1. Convex Functions; 1.1 One-Variable Convex Functions; 1.2 Convex Functions on a Normed Linear Space; 1.3 Convex Functions of Higher Order; 1.4 Functions Convex with Respect to an ECT System of Functions; 1.5 Inequalities Involving Derivatives and Differences; Chapter 2. Jensen's and Jensen-Steffensen's Inequalities; 2.1 Jensen's Inequality; 2.2 Jensen-Steffensen's Inequality
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2.3 Companion Inequalities of Jensen's and Jensen-Steffensen's Inequalities2.4 Higher-Order Jensen-Type Inequalities; Chapter 3. Reversals, Refinements, and Converses of Jensen's and Jensen-Steffensen's Inequalities; 3.1 Reversals of Jensen's and Jensen-Steffensen's Inequalities; 3.2 Some Refinements of Jensen's and Jensen-Steffensen's Inequalities; 3.3 Converses of Jensen's Inequality; Chapter 4. Applications of Jensen's Inequality to Means and Hölder's Inequalities; 4.1 Inequalities for Means; 4.2 Hölder's and Minkowski's Inequalities; 4.3 Dresher's Inequality; 4.4 Beckenbach's Inequality
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4.5 Aczél's and Related Inequalities4.6 Further Generalizations of Hölder's and Minkowski's Inequalities; 4.7 Some Inequalities for Complex Functionals and Norms; Chapter 5. Hermite-Hadamard's and Jensen-Petrović's Inequalities; 5.1 Hermite-Hadamard's Inequality; 5.2 Jensen-Petrović's Inequalities; Chapter 6. Popoviciu's, Burkill's, and Steffensen's Inequalities; 6.1 Inequalities of Popoviciu and Burkill; 6.2 Steffensen's Inequality; Chapter 7. Cebyšev-Grüss', Favard's, Berwald's, Gauss-Winckler's, and Related Inequalities; 7.1 Čebyšev-Grüss Inequality
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7.2 Favard's, Berwald's, Gauss-Winckler's, and Related InequalitiesChapter 8. Hardy's, Hilbert's, Opial's, Young's, Nanson's, and Related Inequalities; 8.1 Hardy's, Hilbert's, Opial's, and Related Inequalities; 8.2 Young's Inequality; 8.3 Nanson's Inequality; Chapter 9. General Linear Inequalities for Convex Sequences and Functions; 9.1 Inequalities for m-Convex Sequences and Functions; 9.2 Some Generalizations and Refinements; Chapter 10. Orderings and Convexity-Preserving Transformations; 10.1 Orderings of Convexity: Generalizations and Related Results; 10.2 Various Results
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Chapter 11. Convex Functions and Geometric Inequalities11.1 Old and New Results via Majorization Theory; 11.2 Concavity via Hyperbolic Forms; Chapter 12. Convexity, Majorization, and Schur-Convexity; 12.1 Majorization and Convex Functions; 12.2 Schur-Convex Functions; 12.3 Multivariate Majorization and Convex Functions; Chapter 13. Convexity and Log-Concavity Related Moment and Probability Inequalities; 13.1 Jensen's Inequality; 13.2 Moment Inequalities for Univariate Random Variables; 13.3 Dimension-Related Inequalities for Exchangeable Random Variables; 13.4 Brunn-Minkowski Inequality
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13.5 A Class of Log-Concave Probability Measures
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English
Weitere Ausg.:
ISBN 0-12-549250-2
Sprache:
Englisch
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