Jungck theorem for triangular maps and related results

M. Grinc, L. Snoha

Abstract

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.


Keywords

Compatible maps; Complete invariance property; Jungck theorem; Jachymski theorem; Fixed point

Subject classification

54H20; 54H25

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1. Common fixed points and invariant approximation for Gregus type contraction mappings
Sumit Chandok, T. D. Narang
Rendiconti del Circolo Matematico di Palermo  vol: 60  issue: 1-2  first page: 203  year: 2011  
doi: 10.1007/s12215-011-0043-5



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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt