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An abstract common fixed point principle and its applications
Published online by Cambridge University Press: 17 April 2009
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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.
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- Research Article
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- Copyright © Australian Mathematical Society 1996
References
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