Auteur
Convex functions play an important role in almost all branches of mathematics, and this book is a thorough introduction to contemporary convex function theory. It covers a large variety of subjects, from the one real variable case (with all its mathematical gems) to some of the most advanced topics such as Choquet's theory, the Prékopa-Leindler type inequalities and their ramifications, as well as the variational approach of partial differential equations and convex programming.

Texte du rabat

Thorough introduction to an important area of mathematics

Contains recent results

Includes many exercises

Résumé
From the reviews:

"This monograph is aimed to serve as an elementary graduate textbook on convex functions. ... Four appendices complete this book. ... A list of exercises is provided at the end of each section. Every chapter is closed by a section with valuable historical remarks and comments on further developments." (Giovanni Alberti, Mathematical Reviews, Issue 2006 m)

"The book is devoted to elementary theory of convex functions. ... The book will be useful to all who are interested in convex functions and their applications." (Peter Zabreiko, Zentralblatt MATH, Vol. 1100 (2), 2007)

"This is a nice little book, providing a new look at the old subject of convexity and treating it from different points of view. As the authors suggest, parts of it can be used for a course on convexity for first year graduate students. ... The book well documents sources of ideas and the origins of results and will be of interest even for specialists in the field; it may also be used as a reference book on the subject." (EMS Newsletter, September, 2006)

"The book could be of interest to those applied mathematicians who feel that such material could be useful to them. ... is intended to be a classroom text, in which each chapter is followed by an extensive 'Comments' section containing some background as well as some additional results. ... it is more suited as a scholarly introduction to convex functions and their many uses. It very much lives up to its subtitle, A Contemporary Approach." (Robert Phelps, SIAM Review, Vol. 49 (1), 2007)

Contenu

Convex Functions on Intervals Comparative Convexity on Intervals Convex Functions on Banach Spaces Choquet's Theory A Background on Convex Sets B Elementary Symmetric Functions C The Convex Programming Problem D The Variational Approach of PDE E Horn's Conjecture