Mann's iteration is the dynamical system defined for a continuous function ![f:[0,1]->[0,1]](/images/equations/MannIteration/Inline1.svg)
,
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with ![x_0 in [0,1]](/images/equations/MannIteration/Inline2.svg)
.
It can also be written
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This iteration always converges to a fixed point of 
.
Mann Iteration
See also
Map Fixed Point, Sharkovsky's TheoremExplore with Wolfram|Alpha
References
Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, pp. 78-79, 2003.Referenced on Wolfram|Alpha
Mann IterationCite this as:
Weisstein, Eric W. "Mann Iteration." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MannIteration.html