Convex Functions and Their Applications: A Contemporary Approach

by Constantin P. Niculescu, Lars-Erik Persson

Overview

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years. These additions are essential for grasping the practical applications of convex function theory in solving contemporary real-world problems.

To reflect these advancements, the material has been meticulously reorganized, with a greater emphasis on topics relevant to current research. Additionally, great care has been taken to ensure that the text remains accessible to a broad audience, including both students and researchers focused on the application of mathematics.

Ideal for undergraduate courses, graduate seminars, or as a comprehensive reference, this book is an indispensable resource for those seeking to understand the extensive potential of convex function theory.

Product Details

ISBN-13:	9783031719660
Publisher:	Springer Nature Switzerland
Publication date:	03/12/2025
Series:	CMS/CAIMS Books in Mathematics , #14
Edition description:	Third Edition 2025
Pages:	494
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Constantin P. Niculescu is Professor Emeritus of Mathematics at the University of Craiova, Romania, and an honorary member of the "Simion Stoilow" Institute of Mathematics of the Romanian Academy.

His research interests include convex analysis, functional analysis, real analysis, history, and heuristics of mathematics. He has authored several books and more than one hundred papers, for which he has been awarded several prizes for research and exposition.

Lars-Erik Persson is Professor of Mathematics at UiT, The Arctic University of Norway, Senior Professor at Karlstad University, Sweden, and Professor Emeritus at Uppsala University, Sweden. He has been the President of the Swedish Mathematical Society His research interests include convex analysis, functional analysis, interpolation theory, Fourier analysis, inequalities and homogenization theory He has authored several books and around 250 papers. He has received several awards for research but also for supervision and teaching.

Table of Contents

Convex Functions at a First Glance.- More on Convex Functions on Intervals.- Convex Sets in Real Linear Spaces.- Convex Functions on a Normed Linear Space.- Differentiable Convex Functions. 6. Convexity and Majorization.- Convexity in Spaces of Matrices.- Convexity in Spaces of Matrices.- Duality and Convex Optimization.- Special Topics in Majorization Theory. Appendices.- Generalized Convexity on Intervals.- Background on Convex Sets.- Elementary Symmetric Functions.- Second Order Differentiability of Convex Functions.- The Variational Approach of PDE.

Editorial Reviews

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)

From the Publisher