Skip to main content
SpringerLink
Log in

Axiomatic and algebraic convexity of regular pairs

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

Two dimensional Chebyshev systems, quoted also as regular pairs, induce convex structures both in an axiomatic and in an algebraic way. The aim of this note is to link these structures, by showing that they coincide.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baron, K., Matkowski, J., Nikodem, K.: A sandwich with convexity. Math. Pannon. 5(1), 139–144 (1994)

    MathSciNet  MATH  Google Scholar 

  2. Barvinok, A.: A Course in Convexity, vol. 54. Graduate Studies in MathematicsAmerican Mathematical Society, Providence (2002)

    MATH  Google Scholar 

  3. Beckenbach, E.F.: Generalized convex functions. Bull. Am. Math. Soc. 43(6), 363–371 (1937)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bessenyei, M., Konkoly, Á., Popovics, B.: Convexity with respect to Beckenbach families. J. Convex Anal. 24(1), 75–92 (2017)

    MathSciNet  MATH  Google Scholar 

  5. Bessenyei, M., Páles, Z.S.: Hadamard-type inequalities for generalized convex functions. Math. Inequal. Appl. 6(3), 379–392 (2003)

    MathSciNet  MATH  Google Scholar 

  6. Bessenyei, M., Popovics, B.: Convexity without convex combinations. J. Geom. 107(1), 77–88 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bessenyei, M., Popovics, B.: Convexity structures induces by Chebyshev systems. Indag. Math. (N.S.) 28(6), 1126–1133 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bessenyei, M., Szokol, P.: Convex separation by regular pairs. J. Geom. 104(1), 45–56 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Carathéodory, C.: Über den variabilitätsbereich der fourierschen konstanten von positiven harmonischen funktionen. Rend. Circ. Mat. Palermo 32, 193–217 (1911)

    Article  MATH  Google Scholar 

  10. Karlin, S., Studden, W.J.: Tchebycheff Systems: With Applications in Analysis and Statistics, vol. XV. Pure and Applied Mathematics‘Wiley, New York (1966)

    MATH  Google Scholar 

  11. Krzyszkowski, J.: Generalized convex sets, Rocznik Nauk.-Dydakt. Prace Mat., No. 14, pp. 59–68 (1997)

  12. Krzyszkowski, J.: Approximately generalized convex functions. Math. Pannon. 12(1), 93–104 (2001)

    MathSciNet  MATH  Google Scholar 

  13. Niculescu, C.P., Persson, L.-E.: Convex Functions and Their Applications. A Contemporary Approach, vol. 23. CMS Books in MathematicsSpringer, New York (2006)

    Book  MATH  Google Scholar 

  14. Nikodem, K., Páles, Z.S.: Generalized convexity and separation theorems. J. Convex Anal. 14(2), 239–247 (2007)

    MathSciNet  MATH  Google Scholar 

  15. Nikodem, K., Wąsowicz, S.Z.: A sandwich theorem and Hyers-Ulam stability of affine functions, Aequ. Math. 49(1–2), 160–164 (1995)

  16. van de Vel, M.L.J.: Theory of Convex Structures, vol. 50. North-Holland Mathematical LibraryNorth-Holland Publishing Co., Amsterdam (1993)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, PF. 400, Debrecen, 4002, Hungary

    Mihály Bessenyei

Authors
  1. Mihály Bessenyei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mihály Bessenyei.

Additional information

This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grants K–111651.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bessenyei, M. Axiomatic and algebraic convexity of regular pairs. J. Geom. 109, 24 (2018). https://doi.org/10.1007/s00022-018-0429-z

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1007/s00022-018-0429-z

Keywords

Mathematics Subject Classification

Search

Navigation