Non-Connected Convexities and Applications

  • Gabriela Cristescu
  • Liana Lupşa

Part of the Applied Optimization book series (APOP, volume 68)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Non-connected convexity properties

    1. Front Matter
      Pages 1-1
    2. Gabriela Cristescu, Liana Lupşa
      Pages 3-21
    3. Gabriela Cristescu, Liana Lupşa
      Pages 23-59
    4. Gabriela Cristescu, Liana Lupşa
      Pages 61-87
    5. Gabriela Cristescu, Liana Lupşa
      Pages 89-111
    6. Gabriela Cristescu, Liana Lupşa
      Pages 113-132
    7. Gabriela Cristescu, Liana Lupşa
      Pages 133-142
    8. Gabriela Cristescu, Liana Lupşa
      Pages 143-152
    9. Gabriela Cristescu, Liana Lupşa
      Pages 153-223
  3. Applications

    1. Front Matter
      Pages 225-225
    2. Gabriela Cristescu, Liana Lupşa
      Pages 227-246
    3. Gabriela Cristescu, Liana Lupşa
      Pages 247-262
    4. Gabriela Cristescu, Liana Lupşa
      Pages 263-283
    5. Gabriela Cristescu, Liana Lupşa
      Pages 285-316
    6. Gabriela Cristescu, Liana Lupşa
      Pages 317-337
  4. Back Matter
    Pages 339-368

About this book

Introduction

Lectori salutem! The kind reader opens the book that its authors would have liked to read it themselves, but it was not written yet. Then, their only choice was to write this book, to fill a gap in the mathematicalliterature. The idea of convexity has appeared in the human mind since the antiquity and its fertility has led to a huge diversity of notions and of applications. A student intending a thoroughgoing study of convexity has the sensation of swimming into an ocean. It is due to two reasons: the first one is the great number of properties and applications of the classical convexity and second one is the great number of generalisations for various purposes. As a consequence, a tendency of writing huge books guiding the reader in convexity appeared during the last twenty years (for example, the books of P. M. Gruber and J. M. Willis (1993) and R. J. Webster (1994)). Another last years' tendency is to order, from some point of view, as many convexity notions as possible (for example, the book of I. Singer (1997)). These approaches to the domain of convexity follow the previous point of view of axiomatizing it (A. Ghika (1955), W. Prenowitz (1961), D. Voiculescu (1967), V. W. Bryant and R. J. Webster (1969)). Following this last tendency, our book proposes to the reader two classifications of convexity properties for sets, both of them starting from the internal mechanism of defining them.

Keywords

Convexity DEX behavior boundary element method classification cognition function functions optimization pattern programming set sets theorem types

Authors and affiliations

  • Gabriela Cristescu
    • 1
  • Liana Lupşa
    • 2
  1. 1.Aurel Vlaicu University of AradAradRomania
  2. 2.Babeş-Bolyai University of Cluj-NapocaCluj-NapocaRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-0003-2
  • Copyright Information Springer-Verlag US 2002
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-4881-8
  • Online ISBN 978-1-4615-0003-2
  • Series Print ISSN 1384-6485
  • About this book