Non-Connected Convexities and Applications

1. Front Matter

   Pages i-xx

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2. Non-connected convexity properties

   1. Front Matter

      Pages 1-1

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   2. The fields of non-connected convexity properties

      • Gabriela Cristescu, Liana Lupşa

      Pages 3-21

   3. Convexity with respect to a set

      • Gabriela Cristescu, Liana Lupşa

      Pages 23-59

   4. Behaviours. Convexity with respect to a behaviour

      • Gabriela Cristescu, Liana Lupşa

      Pages 61-87

   5. Convexity with respect to a set and two behaviours

      • Gabriela Cristescu, Liana Lupşa

      Pages 89-111

   6. Convexities defined by means of distance functions

      • Gabriela Cristescu, Liana Lupşa

      Pages 113-132

   7. Induced convexity

      • Gabriela Cristescu, Liana Lupşa

      Pages 133-142

   8. Convexity defined by means of given function

      • Gabriela Cristescu, Liana Lupşa

      Pages 143-152

   9. Classification of the convexity properties

      • Gabriela Cristescu, Liana Lupşa

      Pages 153-223

3. Applications

   1. Front Matter

      Pages 225-225

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   2. Applications in pattern recognition

      • Gabriela Cristescu, Liana Lupşa

      Pages 227-246

   3. Alternative theorems and integer convex sets

      • Gabriela Cristescu, Liana Lupşa

      Pages 247-262

   4. Various types of generalized convex functions

      • Gabriela Cristescu, Liana Lupşa

      Pages 263-283

   5. Applications in optimisation

      • Gabriela Cristescu, Liana Lupşa

      Pages 285-316

   6. Applications in pharmaco-economics

      • Gabriela Cristescu, Liana Lupşa

      Pages 317-337

4. Back Matter

   Pages 339-368

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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.

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

• Aurel Vlaicu University of Arad, Arad, Romania

  Gabriela Cristescu

• Babeş-Bolyai University of Cluj-Napoca, Cluj-Napoca, Romania

  Liana Lupşa

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