Abstract
We discuss a fixed point theorem for a function f mapping a complete metric space X into itself. For all \({x \in X}\) the iterates of f(x) are shown to converge to \({{x_{\star} = f(x_{\star})}}\) and an explicit estimate of the convergence rate is given.
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Boyd D.W., Wong J.S.: On nonlinear contractions. Proc. Amer. Math. Soc. 20, 458–464 (1969)
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To Professor Richard Palais
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Pata, V. A fixed point theorem in metric spaces. J. Fixed Point Theory Appl. 10, 299–305 (2011). https://doi.org/10.1007/s11784-011-0060-1
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DOI: https://doi.org/10.1007/s11784-011-0060-1