Skip to main content
SpringerLink
Log in

Fixed Points and Order

  • Chapter
  • First Online:
Elementary Fixed Point Theorems

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

  • 1084 Accesses

Abstract

This chapter deals with fixed points of mappings on partially ordered sets (vide Definition 1.1.10) under diverse hypotheses.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 39.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abian, A.: Fixed point theorems of the mappings of partially ordered sets. Rend. Circ. Mat. Palermo 20, 139–142 (1971)

    Article  MathSciNet  Google Scholar 

  2. Abian, A.: A fixed point theorem equivalent to the axiom of choice. Arch. Math. Log. 25, 173–174 (1985)

    Article  MathSciNet  Google Scholar 

  3. Andres, J., Pastor, K., Snyrychova, P.: Simple fixed point theorems on linear continua. Cubo 10, 27–43 (2008)

    MathSciNet  MATH  Google Scholar 

  4. Blair, C., Roth, A.E.: An extension and simple proof of a constrained lattice fixed point theorem. Algebra Universalis 9, 131–132 (1979)

    Article  MathSciNet  Google Scholar 

  5. Bourbaki, N.: Sur le theoreme de Zorn. Arch. Math. 2, 434–437 (1949–1950)

    Article  MathSciNet  Google Scholar 

  6. Chitra, A., Subrahmanyam, P.V.: Remarks on a nonlinear complementarity problem. J. Optim. Theory Appl. 53, 297–302 (1987)

    Article  MathSciNet  Google Scholar 

  7. Davis, A.: A characterization of complete lattices. Pac. J. Math. 5, 311–319 (1955)

    Article  MathSciNet  Google Scholar 

  8. Friedman, A.: Partial Differential Equations of Parabolic Type. Prentice-Hall Inc., Englewood Cliffs (1964)

    Google Scholar 

  9. Fujimoto, T.: Nonlinear complementarity problems in a function space. SIAM J. Control Optim. 18, 621–623 (1980)

    Article  MathSciNet  Google Scholar 

  10. Kelley, J.L.: General Topology. Springer, Berlin (1975)

    MATH  Google Scholar 

  11. Knaster, B.: Un theoreme sur les functions d’ensembles. Ann. Soc. Polon. Math. 5, 133–134 (1927–1928)

    Google Scholar 

  12. Merrifield, K., Stein, J.D.: Common fixed points of two isotone maps on a complete lattice. Czechoslov. Math. J. 49(124), 849–866 (1999)

    Article  MathSciNet  Google Scholar 

  13. Moroianu, M.: On a theorem of Bourbaki. Rend. Circ. Math. Palermo 20, 139–142 (1971)

    Article  Google Scholar 

  14. Roth, A.E.: A lattice fixed-point theorem with constraints. Bull. Am. Math. Soc. 81, 136–138 (1975)

    Article  MathSciNet  Google Scholar 

  15. Schäfer, U.: An existence theorem for a parabolic differential equation in \(\ell ^\infty (A)\) based on the Tarski fixed point theorem. Demonstr. Math. 30, 461–464 (1997)

    Google Scholar 

  16. Stein, J.D.: Fixed points of inequality preserving maps in complete lattices. Czechoslov. Math. J. 49(124), 35–43 (1999)

    Article  MathSciNet  Google Scholar 

  17. Stein, J.D.: A systematic generalization procedure for fixed point theorems. Rocky Mt. J. Math. 30, 735–754 (2000)

    Article  MathSciNet  Google Scholar 

  18. Tarski, A.: A lattice theoretical fix point theorem and its applications. Pac. J. Math. 5, 285–309 (1955)

    Article  Google Scholar 

  19. Zermelo, E.: Neuer Beweis fur die Moglichkeit einer Wohlordnung. Math. Ann. 15, 107–128 (1908)

    MATH  Google Scholar 

  20. Zorn, M.: A remark on method in transfinite algebra. Bull. Am. Math. Soc. 41, 667–670 (1935)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India

    P. V. Subrahmanyam

Authors
  1. P. V. Subrahmanyam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. V. Subrahmanyam .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Subrahmanyam, P.V. (2018). Fixed Points and Order. In: Elementary Fixed Point Theorems. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-3158-9_3

Download citation

Publish with us

Policies and ethics

Search

Navigation