On the Banach Contraction Principle for Multivalued Mappings

  • Jan Andres
  • Lech Górniewicz
Conference paper

Abstract

We give a survey of recent results concerning the Banach contraction principle for multivalued mappings. Nevertheless, this survey contains also some new so far unpublished results. The following main problems are concerned:
  1. (i)

    existence of fixed points

     
  2. (ii)

    topological structure of the set of fixed points

     
  3. (iii)

    generalized essentiality.

    Some applications, mainly to differential inclusions, and open problems are presented as well

     

Keywords

set-valued maps fixed points iterated multifunction systems equations with multivalued right-hand sides 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jan Andres
    • 1
  • Lech Górniewicz
    • 2
  1. 1.Department of MathAnalysis, Faculty of Science, Palacký UniversityOlomouc-HejčínCzech Republic
  2. 2.Faculty of Mathematics and Computer SciencesNicholas Copernicus UniversityToruńPoland

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