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An abstract common fixed point principle and its applications

Published online by Cambridge University Press:  17 April 2009

Jacek R. Jachymski
Jacek R. Jachymski
Affiliation:
Institute of Mathematics, Technical University of Lódź, Żwirki 36, 90–924 Łódź, Poland, e-mail: [email protected]
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We establish a common fixed point principle for a commutative family of self-maps on an abstract set. This principle easily yields the Markoff-Kakutani theorem for affine maps, Kirk's theorem for nonexpansive maps and Cano's theorem for maps on the unit interval. As another application we obtain a new common fixed point theorem for a commutative family of maps on an arbitrary interval, which generalises an earlier result of Mitchell.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 1 , February 1996 , pp. 13 - 19
Copyright
Copyright © Australian Mathematical Society 1996

References

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