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Rates of asymptotic regularity for the alternating Halpern–Mann iteration

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Abstract

In this paper we extend to UCW-hyperbolic spaces the quantitative asymptotic regularity results for the alternating Halpern–Mann iteration obtained by Dinis and the second author for CAT(0) spaces. These results are new even for uniformly convex normed spaces. Furthermore, for a particular choice of the parameter sequences, we compute linear rates of asymptotic regularity in W-hyperbolic spaces and quadratic rates of T- and U-asymptotic regularity in CAT(0) spaces.

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Acknowledgements

The first author thanks Adriana Nicolae for useful discussions on the subject of the paper. The second author was supported by the German Science Foundation (DFG Project KO 1737/6-2).

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Authors and Affiliations

  1. LOS, Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

    Laurenţiu Leuştean

  2. Department of Mathematics, Technische Universität Darmstadt, Darmstadt, Germany

    Pedro Pinto

  3. Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

    Laurenţiu Leuştean

  4. Institute for Logic and Data Science, Bucharest, Romania

    Laurenţiu Leuştean

Authors
  1. Laurenţiu Leuştean
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  2. Pedro Pinto
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Correspondence to Laurenţiu Leuştean.

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Leuştean, L., Pinto, P. Rates of asymptotic regularity for the alternating Halpern–Mann iteration. Optim Lett 18, 529–543 (2024). https://doi.org/10.1007/s11590-023-02002-y

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