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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Firmly nonexpansive mappings in classes of geodesic spaces
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by David Ariza-Ruiz, Laurenţiu Leuştean and Genaro López-Acedo PDF
Trans. Amer. Math. Soc. 366 (2014), 4299-4322 Request permission

Abstract:

Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) $W$-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations.
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  • David Ariza-Ruiz
  • Affiliation: Departamento Análisis Matemático, Fac. Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain
  • Email: dariza@us.es
  • Laurenţiu Leuştean
  • Affiliation: Simion Stoilow Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, RO-014700 Bucharest, Romania
  • ORCID: 0000-0003-4154-8761
  • Email: Laurentiu.Leustean@imar.ro
  • Genaro López-Acedo
  • Affiliation: Departamento Análisis Matemático, Fac. Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain
  • Email: glopez@us.es
  • Received by editor(s): March 10, 2012
  • Received by editor(s) in revised form: May 29, 2012, and September 22, 2012
  • Published electronically: March 26, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 4299-4322
  • MSC (2010): Primary 47H09, 47H10, 53C22; Secondary 03F10, 47H05, 90C25, 52A41
  • DOI: https://doi.org/10.1090/S0002-9947-2014-05968-0
  • MathSciNet review: 3206460