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Convex Functions and Their Applications

A Contemporary Approach

  • Constantin P. Niculescu
  • Lars-Erik Persson

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Constantin P. Niculescu, Lars-Erik Persson
    Pages 1-6
  3. Constantin P. Niculescu, Lars-Erik Persson
    Pages 7-64
  4. Constantin P. Niculescu, Lars-Erik Persson
    Pages 65-100
  5. Constantin P. Niculescu, Lars-Erik Persson
    Pages 101-176
  6. Constantin P. Niculescu, Lars-Erik Persson
    Pages 177-202
  7. Back Matter
    Pages 203-255

About this book

Introduction

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.

Keywords

Convexity Mathematica banach spaces differential equation partial differential equation

Authors and affiliations

  • Constantin P. Niculescu
    • 1
  • Lars-Erik Persson
    • 2
  1. 1.Department of MathematicsUniversity of CraiovaCraiovaRomania
  2. 2.Department of MathematicsLuleå University of TechnologyLuleåSweden

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-31077-0
  • Copyright Information Springer-Verlag New York 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-24300-9
  • Online ISBN 978-0-387-31077-0
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152
  • Buy this book on publisher's site
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