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Convex Functions and Their Applications: A Contemporary Approach (CMS Books in Mathematics)

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Synopses & Reviews

Publisher Comments:

Convex functions play an important role in many branches of mathematics, as well as other areas of science and engineering. The present text is aimed to a thorough introduction to contemporary convex function theory, which entails a powerful and elegant interaction between analysis and geometry.  A large variety of subjects are covered, from one real variable case (with all its mathematical gems) to some of the most advanced topics such as the convex calculus, Alexandrov's Hessian, the variational approach of partial differential equations, the Prékopa-Leindler type inequalities and Choquet's theory. This book can be used for a one-semester graduate course on Convex Functions and Applications, and also as a valuable reference and source of inspiration for researchers working with convexity.  The only prerequisites are a background in advanced calculus and linear algebra.  Each section ends with exercises, while each chapter ends with comments covering supplementary material and historical information.  Many results are new, and the whole book reflects the authors' own experience, both in teaching and research. About the authors: Constantin P. Niculescu is a Professor in the Department of Mathematics at the University of Craiova, Romania. Dr. Niculescu directs the Centre for Nonlinear Analysis and Its Applications and also the graduate program in Applied Mathematics at Craiova. He received his doctorate from the University of Bucharest in 1974. He published in Banach Space Theory, Convexity Inequalities and Dynamical Systems, and has received several prizes both for research and exposition. Lars Erik Persson is Professor of Mathematics at Luleå University of Technology and Uppsala University, Sweden. He is the director of Center of Applied Mathematics at Luleå, a member of the Swedish National Committee of Mathematics at the Royal Academy of Sciences, and served as President of the Swedish Mathematical Society (1996-1998). He received his doctorate from Umeå University in 1974. Dr. Persson has published on interpolation of operators, Fourier analysis, function theory, inequalities and homogenization theory. He has received several prizes both for research and teaching.

Synopsis:

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Synopsis:

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 Prékopa-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.

Table of Contents

* 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

Product Details

ISBN:
9781441920287
Author:
Niculescu, Constantin
Publisher:
Springer
Author:
Persson, Lars-Erik
Subject:
Functional Analysis
Subject:
Real functions
Subject:
Convex and Discrete Geometry
Subject:
Convex and Discrete Geometry <P>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 variab
Subject:
Mathematics-Analysis General
Subject:
Mathematical Analysis
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2006
Series:
CMS Books in Mathematics
Publication Date:
20101119
Binding:
TRADE PAPER
Language:
English
Pages:
271
Dimensions:
235 x 155 mm 416 gr

Related Subjects

Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » Geometry » General

Convex Functions and Their Applications: A Contemporary Approach (CMS Books in Mathematics) New Trade Paper
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Product details 271 pages Not Avail - English 9781441920287 Reviews:
"Synopsis" by , Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
"Synopsis" by , 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 Prékopa-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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