Systems of random mappings with a common fixed point

Moshe Kam, Wei Chang, Chris Rorres

Research output: Contribution to journalArticlepeer-review

Abstract

Mappings from a set of Lipschitz-continuous mappings are applied successively on an initial point x 0 in a complete metric space. All mappings possess the same fixed point x and are applied at random with repetitions. A lower bound is found for the probability that the system’s state after n iterations, xn, is within a p-neighbour-hood of the common fixed point x. Moreover, sufficient conditions on the Lipschitz constants and on the probabilities of occurrence of the mappings which guaranteee convergence of the system’s state to x in the mean-square sense are found.

Original languageEnglish (US)
Pages (from-to)2113-2119
Number of pages7
JournalInternational Journal of Systems Science
Volume23
Issue number11
DOIs
StatePublished - Nov 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications

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