Skip to main content

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 27))

Abstract

In this paper some notions of convexity with respect to a given set in a convexity space are introduced. Some properties of these sets are given. Also induced convexity concepts are defined.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cristescu G., “Convexities with respect to a set and two behaviours,” Proc. Sci. Com. Meeting of the “Aurel Vlaicu” University, Third Edition, Arad, 16–17 Mai 1996, Vol. 14 A (to appear).

    Google Scholar 

  2. Lupşa L., “Asupra unei noţiuni de convexitate,” Seminarul itinerant de ecuaţii funcţionale şi convexitate, 7-8 noiembrie 1980, Timişoara, pp. 127–135.

    Google Scholar 

  3. Lupşa L., “Separation of strong convex sets,” Itinerant Seminar on Functional Equation, Approximation and Convexity, Cluj-Napoca, 1983, pp. 85–86.

    Google Scholar 

  4. Lupşa L., “Some types of convexity with respect to a given set,” “Babeş-Bolyai” University, Cluj-Napoca, Seminar on Optimization Theory, Report no. 8, 1986, pp. 89–114.

    Google Scholar 

  5. Lupşa L., “I-points with respect to a given set,” Itinerant Seminar on Functional Equations, Approximation and Convexity, Iaşi, 26 oct. 1986, pp. 32–35.

    Google Scholar 

  6. Lupşa L., Duca E., Duca D., “On the structure of the set of dominated and nondominated in an optimization problem,” Revue d’Anal. num. et la théorie de l’approximation, 1993, 22, 2,pp. 193–199.

    MATH  Google Scholar 

  7. Martínez-Legaz J.-E., Singer M., “Multiorder convexity,” Appl. Geom. Discr. Math., 1991, 4, pp. 471–488.

    Google Scholar 

  8. Soltan V.P., “Introduction to the Axiomatic Convexity Theory,” Ştiinţa, Chişinău, 1984 (in russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Kluwer Academic Publishers

About this chapter

Cite this chapter

Blaga, L., Lupşa, L. (1998). Convexity Space with Respect to a Given Set. In: Crouzeix, JP., Martinez-Legaz, JE., Volle, M. (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3341-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3341-8_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3343-2

  • Online ISBN: 978-1-4613-3341-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics