Convex functions play an important role in almost all branches
of mathematics as well as other areas of science and engineering.
This book is a thorough introduction to contemporary convex
function theory addressed to all people whose research or teaching
interests intersect with the field of convexity. 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 Pr kopa-Leindler type inequalities and their
ramifications, as well as the variational approach of partial
differential equations and convex programming. Many results are new
and the whole book reflects the authors own experience, both in
teaching and research. The book can serve as a reference and source
of inspiration to researchers in several branches of mathematics
and engineering and it can also be used for graduate courses.
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