Open Access

A Fixed Point Theorem Based on Miranda

Fixed Point Theory and Applications20072007:078706

DOI: 10.1155/2007/78706

Received: 5 June 2007

Accepted: 1 October 2007

Published: 5 December 2007


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


Authors’ Affiliations

Institut für Angewandte und Numerische Mathematik, Fakultät für Mathematik, Universität Karlsruhe (TH)


  1. Miranda C: Un'osservazione su un teorema di Brouwer. Bollettino dell'Unione Matematica Italiana 1940, 3: 5–7.MathSciNetMATHGoogle 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.MathSciNetMATHGoogle Scholar
  3. Kioustelidis JB: Algorithmic error estimation for approximate solutions of nonlinear systems of equations. Computing 1978,19(4):313–320. 10.1007/BF02252029MathSciNetView ArticleMATHGoogle 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-120006697MathSciNetView ArticleMATHGoogle 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.MathSciNetMATHGoogle 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.MathSciNetMATHGoogle Scholar
  7. Avramescu C: A generalization of Miranda's theorem. Seminar on Fixed Point Theory Cluj-Napoca 2002, 3: 121–127.MathSciNetMATHGoogle Scholar
  8. Avramescu C: Some remarks about Miranda's theorem. Analele Universitatii din Craiova. Seria Matematica Informatica 2000, 27: 6–13.MathSciNetMATHGoogle Scholar


© Uwe Schäfer 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.