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Necessary and sufficient fixed point critera involving attractors
Published online by Cambridge University Press: 17 April 2009
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Let f be a continuous self-map on a complete metric space X and p ∈ X. Let c be a positive real. Equivalent conditions are given for the singleton {p} to be an attractor of a set of c−fixed points of f. We also establish equivalent conditions for the existence of a contractive fixed point of f. These results subsume a body of fixed point theorems.
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- Copyright © Australian Mathematical Society 1993