On the largest common fixed point of a commuting family of isotone maps

Teck-Cheong Lim

doi:10.3934/proc.2005.2005.621

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2005, Volume 2005: 621-623. Doi: 10.3934/proc.2005.2005.621 open access

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On the largest common fixed point of a commuting family of isotone maps

Teck-Cheong Lim^1,

1.
Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030

Received: August 31, 2004

Revised: March 31, 2005

Published: August 2005

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Abstract

We prove that in a complete partially ordered set with a largest point, every commutative family of isotones has the largest common fixed point. This result for a single mapping was used recently by Ok (2004) to study fixed set theory and its applications in economics.

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Mathematics Subject Classification: Primary: 47H10; Secondary: 06A06.

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