- Boca Raton : CRC Press, 2015
- xiii, 161 p. ; ill., 23 cm
- Textbooks in mathematics .
Includes bibliographical references and index.
Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.Convex Analysis introduces analytic tools for studying convexity and provides analytical applications of the concept. The book includes a general background on classical geometric theory which allows readers to obtain a glimpse of how modern mathematics is developed and how g.
Convex geometry Functional analysis Operator theory Discrete geometry Convex functions Brunn-Minkowski inequality Defining function Exhaustion function Factorial function Gamma function Hausdorff distance Krein-Milman theorem Linear programming Mini Max theorem Minikowski functional Ortho -convex set Subharmonic functions Targent directions Approximation