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Hilbert's metric and positive contraction mappings in a Banach space

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References

  1. Bauer, F. L., An elementary proof of the Hopf inequality for positive operators. Numerische Math. 7, 331–337 (1965)

    Google Scholar 

  2. Bauer, F. L., E. Deutsch, & J. Stoer, Abschätzungen für die Eigenwerte positiver linearer Operatoren. Linear Algebra and its Applications 2, 275–301 (1969)

    Google Scholar 

  3. Birkhoff, G., Extensions of Jentzch's Theorem. Trans. Amer. Math. Soc. 85, 219–227 (1957)

    Google Scholar 

  4. Birkhoff, G., Uniformly semi-primitive multiplicative processes. Trans. Amer. Math. Soc. 104, 37–51 (1962)

    Google Scholar 

  5. Birkhoff, G., Uniformly semi-primitive multiplicative processes II. J. Math. Mech. 14, 507–512 (1965)

    Google Scholar 

  6. Birkhoff, G., & L. Kotin, Essentially positive systems of linear differential equations. Bull. Amer. Math. Soc. 71, 771–772 (1965)

    Google Scholar 

  7. Birkhoff, G., & L. Kotin, Linear second order differential equations of positive type. J. d'Analyse Math. 18, 43–52 (1967)

    Google Scholar 

  8. Birkhoff, G., & L. Kotin, Third order positive cyclic systems of linear differential equations. J. Diff. Eq. 5, 182–196 (1969)

    Google Scholar 

  9. Bushell, P. J., On systems of linear ordinary differential equations and the uniqueness of monotone solutions. J. London Math. Soc. (2) 5, 235–239 (1972)

    Google Scholar 

  10. Bushell, P. J., On the projective contraction ratio for positive linear mappings. J. London Math. Soc. (2) 6, 256–258 (1963)

    Google Scholar 

  11. Bushell, P. J., On solutions of the matrix equation T′ AT= A 2. Linear Algebra and its Applications (to appear)

  12. Bushell, P. J., On solutions in a cone of ordinary differential equations in an ordered Banach space (to appear)

  13. Hilbert, D., Über die gerade Linie als kürzeste Verbindung zweier Punkte. Math. Ann. 46, 91–96 (1895)

    Google Scholar 

  14. Karlin, S., Mathematical Methods and Theory in Games, Programming and Economics, Vol. I. Reading, Mass.: Addison-Wesley 1959

    Google Scholar 

  15. Klein, F., Ueber die sogenannte Nicht-Euklidische Geometrie. Math. Ann. 4, 573–625 (1871)

    Google Scholar 

  16. Krasnoselskii, M. A., Positive Solutions of Operator Equations. Groningen, The Netherlands: Noordhoff 1964

    Google Scholar 

  17. Ostrowski, A. M., Positive matrices and functional analysis. Recent Advances in Matrix Theory. Madison: University of Wisconsin Press, 1964

    Google Scholar 

  18. Samuelson, H., On the Perron-Frobenius Theorem. Mich. Math. J. 4, 57–59 (1957)

    Google Scholar 

  19. Thompson, A. C., On certain contraction mappings in a partially ordered vector space. Proc. Amer. Math. Soc. 14, 438–443 (1963)

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Division, University of Sussex, Falmer, Brighton

    P. J. Bushell

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  1. P. J. Bushell
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Communicated by J. Serrin

The author's work was supported in part by the United Kingdom Science Research Council Grant No. B/RG/28436.

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Bushell, P.J. Hilbert's metric and positive contraction mappings in a Banach space. Arch. Rational Mech. Anal. 52, 330–338 (1973). https://doi.org/10.1007/BF00247467

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  • DOI: https://doi.org/10.1007/BF00247467

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