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Firm non-expansive mappings in weak metric spaces

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Abstract

We introduce the notion of a firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm non-expansive mappings, the minimal displacement, the linear rate of escape, and the asymptotic step size are all equal. This generalises a theorem by Reich and Shafrir.

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Acknowledgements

The first author acknowledges financial support from the Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters, and from the Otto A. Malm Foundation.

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  1. Inria and CMAP, Ecole Polytechnique, CNRS, 91128, Palaiseau, France

    Armando W. Gutiérrez & Cormac Walsh

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  1. Armando W. Gutiérrez
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  2. Cormac Walsh
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Correspondence to Armando W. Gutiérrez.

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Gutiérrez, A.W., Walsh, C. Firm non-expansive mappings in weak metric spaces. Arch. Math. 119, 389–400 (2022). https://doi.org/10.1007/s00013-022-01759-5

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  • DOI: https://doi.org/10.1007/s00013-022-01759-5

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