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"Convexity of sets and functions are extremely simple notions to define, so it may be somewhat surprising the depth and breadth of ideas that these notions give rise to. It turns out that convexity is central to a vast number of applied areas, including Statistical Mechanics, Thermodynamics, Mathematical Economics, and Statistics,and that many inequalities, including Hl̲der's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hl̲der, Minkowski, and Jensen), the Hahn-Banach theorem as a statement about extending tangents to convex functions, and the introduction of two constructions that will play major roles later in this book: the Minkowski gauge of a convex set and the Legendre transform of a function"--
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Convex domains, Mathematical analysisEdition | Availability |
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Convexity: an analytic viewpoint
2011, Cambridge University Press
in English
1107007313 9781107007314
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Table of Contents
Edition Notes
Includes bibliographical references (p. [321]-338) and index.
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Feedback?June 29, 2019 | Edited by MARC Bot | import existing book |
October 20, 2011 | Created by LC Bot | import new book |