Inexact orbits of nonexpansive mappings with nonsummable errors

Abstract

Given a nonexpansive mapping which maps a closed subset of a complete metric space into the space, we study the convergence of its inexact iterates to its fixed point set in the case where the errors are nonsummable. Previous results in this direction concerned nonexpansive self-mappings of the complete metric space and inexact iterates with summable errors.

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Acknowledgements

The first author was partially supported by the Israel Science Foundation (Grant No. 820/17), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund. Both authors are grateful to an anonymous referee for several useful comments and helpful suggestions.

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Correspondence to Simeon Reich.

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Reich, S., Zaslavski, A.J. Inexact orbits of nonexpansive mappings with nonsummable errors. Anal.Math.Phys. 10, 19 (2020). https://doi.org/10.1007/s13324-020-00363-6

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Keywords

  • Complete metric space
  • Fixed point
  • Inexact iteration
  • Nonexpansive mapping

Mathematics Subject Classification

  • 47H09
  • 47H10
  • 54E50