Skip to main content
Log in

Existence of common fixed points for abelian families of discontinuous operators

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literature Cited

  1. A. A. Markov, “Some theorems on abelian sets,” Dokl. Akad. Nauk SSSR,10, No. 8, 299–301 (1936).

    Google Scholar 

  2. M. G. Krein and M. A. Rutman, “Linear operators leaving invariant a cone in Banach space,” Usp. Matem. Nauk,3, No. 1, 3–95 (1948).

    Google Scholar 

  3. Yu. M. Berezanskii and S. G. Krein, “Hypercomplex systems with a compact basis,” Ukrainsk. Matem. Zh.,3, No. 2 (1951).

  4. I. A. Bakhtin, “Analysis of equations with positive operators,” Doctoral Dissertation [in Russian], Voronezh (1966).

  5. R. DeMar, “Common fixed points for commuting contraction mappings,” Pacif. J. Math.,13, 1139–1144 (1963).

    Google Scholar 

  6. B. Z. Bulikh, Introduction to the Theory of Semiordered Spaces [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  7. M. A. Krasnosel'skii, Positive Solutions to Operator Equations [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  8. I. A. Bakhtin, “A single criterion for normality of a cone,” [in Russian], Third Seminar on Functional Analysis, Voronezh, No. 6, 19 (1958).

    Google Scholar 

  9. I. A. Bakhtin, “Geometry of cones in Banach space,” Sibirsk. Matem. Zh.,6, No. 2, 262–270 (1965).

    Google Scholar 

  10. I. A. Bakhtin, “Existence of common eigenvectors for a commutative family of linear operators,” Matem. Sb.,109, No. 2, 267–278 (1965).

    Google Scholar 

  11. I. A. Bakhtin, M. A. Krasnosel'skii, and V. Ya. Stetsenko, “Continuity of linear positive operators,” Sibirsk. Matem. Zh.,3, No. 1, 156–160 (1962).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 13, No. 2, pp. 243–251, March–April, 1972.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bakhtin, I.A. Existence of common fixed points for abelian families of discontinuous operators. Sib Math J 13, 167–172 (1972). https://doi.org/10.1007/BF00971605

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00971605

Navigation