Skip to main content
  • Research Article
  • Open access
  • Published:

A Fixed Point Theorem Based on Miranda

Abstract

A new fixed point theorem is proved by using the theorem of Miranda.

[1234567812345678]

References

  1. Miranda C: Un'osservazione su un teorema di Brouwer. Bollettino dell'Unione Matematica Italiana 1940, 3: 5–7.

    MathSciNet  MATH  Google Scholar 

  2. Vrahatis MN: A short proof and a generalization of Miranda's existence theorem. Proceedings of the American Mathematical Society 1989,107(3):701–703.

    MathSciNet  MATH  Google Scholar 

  3. Kioustelidis JB: Algorithmic error estimation for approximate solutions of nonlinear systems of equations. Computing 1978,19(4):313–320. 10.1007/BF02252029

    Article  MathSciNet  MATH  Google Scholar 

  4. Mayer J: A generalized theorem of Miranda and the theorem of Newton-Kantorovich. Numerical Functional Analysis and Optimization 2002,23(3–4):333–357. 10.1081/NFA-120006697

    Article  MathSciNet  MATH  Google Scholar 

  5. Alefeld G, Frommer A, Heindl G, Mayer J: On the existence theorems of Kantorovich, Miranda and Borsuk. Electronic Transactions on Numerical Analysis 2004, 17: 102–111.

    MathSciNet  MATH  Google Scholar 

  6. Pavel NH: Theorems of Brouwer and Miranda in terms of Bouligand-Nagumo fields. Analele Stiintifice ale Universitatii Al. I. Cuza din Iasi. Serie Noua. Matematica 1991,37(2):161–164.

    MathSciNet  MATH  Google Scholar 

  7. Avramescu C: A generalization of Miranda's theorem. Seminar on Fixed Point Theory Cluj-Napoca 2002, 3: 121–127.

    MathSciNet  MATH  Google Scholar 

  8. Avramescu C: Some remarks about Miranda's theorem. Analele Universitatii din Craiova. Seria Matematica Informatica 2000, 27: 6–13.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Uwe Schäfer.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Schäfer, U. A Fixed Point Theorem Based on Miranda. Fixed Point Theory Appl 2007, 078706 (2007). https://doi.org/10.1155/2007/78706

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/78706

Keywords