Skip to main content
Fixed Point Theory and Algorithms for Sciences and Engineering
Download PDF
  • Research Article
  • Open access
  • Published:

Two topological definitions of a Nielsen number for coincidences of noncompact maps

Fixed Point Theory and Applications volume 2004, Article number: 480951 (2004) Cite this article

Abstract

The Nielsen number is a homotopic invariant and a lower bound for the number of coincidences of a pair of continuous functions. We give two homotopic (topological) definitions of this number in general situations, based on the approaches of Wecken and Nielsen, respectively, and we discuss why these definitions do not coincide and correspond to two completely different approaches to coincidence theory.

Author information

Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, Olomouc-Hejčín, 779 00, Czech Republic

    Jan Andres

  2. Department of Mathematics, University of Würzburg, Am Hubland, Würzburg, D-97074, Germany

    Martin Väth

  3. Fachbereich Mathematik und Informatik (WE1), Freie Universität Berlin, Arnimallee 2-6, Berlin, 14195, Germany

    Martin Väth

Authors
  1. Jan Andres
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Väth
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan Andres.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andres, J., Väth, M. Two topological definitions of a Nielsen number for coincidences of noncompact maps. Fixed Point Theory Appl 2004, 480951 (2004). https://doi.org/10.1155/S1687182004308119

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1155/S1687182004308119