Constructions, Characterizations and Counterexamples
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- Jonathan M. Borwein, University of Newcastle, New South Wales
- Jon D. Vanderwerff, La Sierra University, California
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Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.Read more
- Unique focus on the functions themselves, rather than convex analysis
- Contains over 600 exercises showing theory and applications
- All material has been class-tested
- A Choice Outstanding Academic Title, 2011
Reviews & endorsements
"Borwein and Vanderwerff's book is particularly impressive due to its enormous breadth and depth. It is a beautiful experience to browse this inspiring book. The reviewer has not seen any source which is even close to presenting so many different and interesting convex functions and corresponding results. This delightful book is a most welcome addition to the library of any convex analyst or of any mathematician with an interest in convex functions."
Heinz H. Bauschke, Mathematical ReviewsSee more reviews
"This masterful book emerges immediately as the de facto canonical source on it subject, and thus as a vital reference for students of Banach space geometry, functional analysis, analytic inequalities, and needless to say, any aspect of convexity. Truly then, anyone interested in nearly any branch of mathematical analysis should at least browse this book."
D.V. Feldman, Choice Magazine
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- Date Published: May 2012
- format: Adobe eBook Reader
- isbn: 9781139106610
- contains: 10 b/w illus. 640 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. Why convex?
2. Convex functions on Euclidean spaces
3. Finer structure of Euclidean spaces
4. Convex functions on Banach spaces
5. Duality between smoothness and strict convexity
6. Further analytic topics
7. Barriers and Legendre functions
8. Convex functions and classifications of Banach spaces
9. Monotone operators and the Fitzpatrick function
10. Further remarks and notes
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