Systems of random iterative continuous mappings with a common fixed point

Wei Chang, Moshe Kam

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

Abstract

A study is made of systems of Lipschitz-continuous mappings which are applied successively on an initial point x0 in a closed, nonempty, complete metric space. All mappings possess the same fixed point x*, and are applied at random with repetitions by choosing a mapping from a finite set of such functions. A lower bound is found on the probability that the system's state after n iterations, xn, is within a ρ-neighborhood of the common fixed point, x*. Conditions are developed that guarantee that the lower bound is (eventually) monotonically increasing in n.

Original languageEnglish (US)
Pages (from-to)872-877
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume1
StatePublished - 1989
Externally publishedYes
EventProceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3) - Tampa, FL, USA
Duration: Dec 13 1989Dec 15 1989

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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