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The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings

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Abstract

In this paper, we provide, in the setting of geodesic spaces, a unified treatment of some convex minimization problems, which allows for a better understanding and, in some cases, improvement of results proved recently in this direction. For this purpose, we analyze the asymptotic behavior of compositions of finitely many firmly nonexpansive mappings focusing on asymptotic regularity and convergence results.

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Acknowledgments

David Ariza and Genaro López were supported by DGES (Grant MTM2012-34847-C02-01), Junta de Andalucía (Grant P08-FQM-03453). Adriana Nicolae was supported by a grant of the Romanian Ministry of Education, CNCS—UEFISCDI, Project Number PN-II-RU-PD-2012-3-0152. Part of this work was carried out while Adriana Nicolae was visiting the University of Seville. She would like to thank the Department of Mathematical Analysis and the Institute of Mathematics of the University of Seville (IMUS) for the hospitality. The authors would also like to thank the referees for their helpful comments.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain

    David Ariza-Ruiz & Genaro López-Acedo

  2. Department of Mathematics, Babeş-Bolyai University, Kogălniceanu 1, 400084, Cluj-Napoca, Romania

    Adriana Nicolae

  3. Simion Stoilow Institute of Mathematics of the Romanian Academy, Research group of the project PD-3-0152, P.O. Box 1-764, 014700, Bucharest, Romania

    Adriana Nicolae

Authors
  1. David Ariza-Ruiz
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  2. Genaro López-Acedo
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  3. Adriana Nicolae
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Correspondence to Genaro López-Acedo.

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Communicated by Sándor Zoltán Németh.

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Ariza-Ruiz, D., López-Acedo, G. & Nicolae, A. The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings. J Optim Theory Appl 167, 409–429 (2015). https://doi.org/10.1007/s10957-015-0710-3

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  • DOI: https://doi.org/10.1007/s10957-015-0710-3

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