Jungck theorem for triangular maps and related results

• Grinc, M. ^[2] ; Snoha, L. ^[1]
  1. [1] Matej Bel University

     Matej Bel University

     Eslovaquia

     
  2. [2] Silesian University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 1, Nº. 1, 2000, págs. 83-92
• Idioma: inglés
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• Resumen

  • We prove that a continuous triangular map G of the n-dimensional cube In has only fixed points and no other periodic points if and only if G has a common fixed point with every continuous triangular map F that is nontrivially compatible with G. This is an analog of Jungck theorem for maps of a real compact interval. We also discuss possible extensions of Jungck theorem, Jachymski theorem and some related results to more general spaces. In particular, the spaces with the fixed point property and the complete invariance property are considered.