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

Pages: 621 - 623, Issue Special, August 2005

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Teck-Cheong Lim - Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, United States (email)

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.

Keywords:  fixed point, isotone map, partially ordered set, commutative family.
Mathematics Subject Classification:  Primary: 47H10; Secondary: 06A06.

Received: September 2004;      Revised: April 2005;      Published: September 2005.