Explores the various classes and their characteristics, treating convex functions in both Euclidean and Banach spaces.

Jonathan M. Borwein is Canada Research Chair in Distributed and Collaborative Research at Dalhousie University, Nova Scotia. He is presently Visiting Professor Laureate at the University of Newcastle, New South Wales.

Preface; 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; References; Index.