Advertisement

Siberian Advances in Mathematics

, Volume 25, Issue 2, pp 124–137 | Cite as

Peano’s theorem and coplanarity points of space curves

  • Yu. G. Nikonorov
Article

Abstract

We study coplanarity points on space differentiable curves and their asymptotic properties. The results make it possible to formulate some general conjectures on the asymptotics of coplanarity points.

Keywords

parametric curve in Euclidean space smooth curve Peano theorem coplanarity point 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Genocchi, Calcolo Differenziale e Principii di Calcolo Integrale, Pubblicato con Aggiunte dal Dr. Giuseppe Peano (Bocca, Turin, 1884).Google Scholar
  2. 2.
    V. V. Ivanov and Yu. G. Nikonorov, “Asymptotic behavior of the Lagrange points in the Taylor formula,” Sib. Mat. Zh. 36, 86 (1995) [Sib. Math. J. 36, 78 (1995)].CrossRefMathSciNetGoogle Scholar
  3. 3.
    Yu. G. Nikonorov, “On the integral mean value theorem,” Sib. Mat. Zh. 34, 150 (1993) [Sib. Math. J. 34, 1135 (1993)].CrossRefMathSciNetGoogle Scholar
  4. 4.
    Yu.G. Nikonorov, “Asymptotics of tangent points for planar curves,” Mat. Tr. 14, 141 (2011) [Sib. Adv.Math. 22, 192 (2012)].MathSciNetGoogle Scholar
  5. 5.
    Yu. G. Nikonorov, “Asymptotic behavior of support points for planar curves,” J. Math. Anal. Appl. 391, 147 (2012).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Yu. G. Nikonorov, “Asymptotics of mean value points in the Schwarz theorem for divided differences,” Mat. Tr. 17, 145 (2014) [Sib. Adv.Math. 25, 56 (2015)].MathSciNetGoogle Scholar
  7. 7.
    G. Peano and H. C. Kennedy, Selected Works of Giuseppe Peano. (Toronto Univ. Press, Toronto, Ont.-Buffalo, N.Y., 1973).Google Scholar
  8. 8.
    A. V. Pogorelov, Differential Geometry (Nauka, Moscow, 1974; Wolters-Noordhoff Publishing, Groningen, 1967).Google Scholar
  9. 9.
    P. K. Sahoo and T. Riedel,Mean Value Theorems and Functional Equations. (World Scientific Publishing Co., New Jersey, 1998).CrossRefMATHGoogle Scholar
  10. 10.
    V. A. Toponogov, Differential Geometry of Curves and Surfaces. A Concise Guide (Birkhauser, Basel, 2005; Fizmatkniga, Moscow, 2012).MATHGoogle Scholar
  11. 11.
    Zhi-Hua Zhang, Yu-Dong Wu, and H. M. Srivastava, “Generalized Vandermonde determinants and mean values,” Appl. Math. Comput. 202, 300 (2008).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Allerton Press, Inc. 2015

Authors and Affiliations

  1. 1.Southern Mathematical Institute of the Vladikavkaz Scientific Center of RASVladikavkazRussia
  2. 2.The Government of the Republic of North Osetia-AlaniaVladikavkazRussia

Personalised recommendations