Generalized Convex Sets

  • Jaroslav Ramík
  • Milan Vlach
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 41)


In this chapter we first generalize convex sets by introducing the concept of starshaped sets, which is “one-step” more general than the concept of convex sets. Then we make further steps generalizing the starshaped sets to obtain path-connected sets, Φ-convex sets and some other types of generalized convex sets. The generalized convex sets will serve as a basis for defining generalized concave and convex functions, which will be introduced in the third chapter. We also pay attention to the separability of starshaped sets.


Convex Cone Nonempty Subset Linear Functional Generalize Convex Finite Family 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Jaroslav Ramík
    • 1
  • Milan Vlach
    • 2
    • 3
  1. 1.School of Business AdministrationSilesian UniversityKarvináCzech Republic
  2. 2.School of Information ScienceJapan Advanced Institute of Science and TechnologyIshikawaJapan
  3. 3.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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