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Iterated nonexpansive mappings

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Abstract

In this paper, we present a further study of iterated nonexpansive mappings, that is, mappings which are nonexpansive along the orbits. This is a wide class of nonlinear mappings including many generalized nonexpansive mappings, such as Suzuki (C)-type generalized nonexpansive mappings and, among others, mappings satisfying the so-called condition (B). In some cases, as for Suzuki (C)-type generalized nonexpansive mappings, the existence of a fixed point is known in the setting of Banach spaces with normal structure. We prove that the same is true for many other classes of iterated nonexpansive mappings.

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Acknowledgements

We are indebted to Professor Łukasz Piasecki for drawing our attention to the facts described in Remark 4.1 and to the anonymous referee for his valuable suggestions to improve the readability of this manuscript.

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Authors and Affiliations

  1. Department of Mathematical Analysis, University of Seville, c/Tarfia s/n., 41012, Sevilla, Spain

    Tomás Domínguez Benavides

  2. Department of Mathematical Analysis, University of Valencia, Dr. Moliner 50, 46100, Burjassot, Valencia, Spain

    Enrique Llorens-Fuster

Authors
  1. Tomás Domínguez Benavides
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  2. Enrique Llorens-Fuster
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Correspondence to Tomás Domínguez Benavides.

Additional information

The authors are partially supported by MCIN, Grant MTM2015-65242-C2 and Junta de Andalucía, Grant FQM-127.

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Domínguez Benavides, T., Llorens-Fuster, E. Iterated nonexpansive mappings. J. Fixed Point Theory Appl. 20, 104 (2018). https://doi.org/10.1007/s11784-018-0579-5

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