Convexity

H. G. Eggleston

doi:10.1017/CBO9780511566172

This account of convexity includes the basic properties of convex sets in Euclidean space and their applications, the theory of convex functions and an outline of the results of transformations and combinations of convex sets. It will be useful for those concerned with the many applications of convexity in economics, the theory of games, the theory of functions, topology, geometry and the theory of numbers.

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Convexity

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Chapter 1 - GENERAL PROPERTIES OF CONVEX SETS
pp 1-32

Chapter 2 - HELLY'S THEOREM AND ITS APPLICATIONS
pp 33-44

Chapter 3 - GENERAL PROPERTIES OF CONVEX FUNCTIONS
pp 45-58

Chapter 4 - APPROXIMATIONS TO CONVEX SETS. THE BLASCHKE SELECTION THEOREM
pp 59-78

Chapter 5 - TRANSFORMATIONS AND COMBINATIONS OF CONVEX SETS
pp 79-102

Chapter 6 - SOME SPECIAL PROBLEMS
pp 103-121

Chapter 7 - SETS OF CONSTANT WIDTH
pp 122-135

Notes
pp 136-138

References
pp 139-140

Index
pp 141-141

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