TY - BOOK AU - Borwein,Jonathan M. AU - Vanderwerff,Jon D. TI - Convex functions: constructions, characterizations and counterexamples T2 - Encyclopedia of mathematics and its applications SN - 9780521850056 PY - 2010/// CY - Cambridge, U. K., New York PB - Cambridge University Press KW - Convex functions KW - Banach spaces KW - Geometry, Non-Euclidean N1 - Includes bibliographical references and index; Why convex? -- Convex functions on Euclidean spaces -- Finer structure of Euclidean spaces -- Convex functions on Banach spaces -- Duality between smoothness and strict convexity -- Further analytic topics -- Barriers and Legendre functions -- Convex functions and classifications of Banach spaces -- Monotone operators and the Fitzpatrick function -- Further remarks and notes ER -