Convex Functions

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. Jon D. Vanderwerff is a Professor of Mathematics at La Sierra University, California.

• 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.

'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 beautiful 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 Reviews