Systems of random iterative continuous mappings with a common fixed point

Wei Chang; Moshe Kam

Systems of random iterative continuous mappings with a common fixed point

Research output: Contribution to journal › Conference article › peer-review

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, x_n, 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 language	English (US)
Pages (from-to)	872-877
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	1
State	Published - 1989
Externally published	Yes
Event	Proceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3) - Tampa, FL, USA Duration: Dec 13 1989 → Dec 15 1989

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Cite this

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title = "Systems of random iterative continuous mappings with a common fixed point",

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.",

author = "Wei Chang and Moshe Kam",

year = "1989",

language = "English (US)",

volume = "1",

pages = "872--877",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0191-2216",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "Proceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3) ; Conference date: 13-12-1989 Through 15-12-1989",

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TY - JOUR

T1 - Systems of random iterative continuous mappings with a common fixed point

AU - Chang, Wei

AU - Kam, Moshe

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

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M3 - Conference article

AN - SCOPUS:0024911626

SN - 0191-2216

VL - 1

SP - 872

EP - 877

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - Proceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3)

Y2 - 13 December 1989 through 15 December 1989

ER -

Systems of random iterative continuous mappings with a common fixed point

Abstract

All Science Journal Classification (ASJC) codes

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