Effective metastability of Halpern iterates in CAT(0) spaces

@article{Kohlenbach2011EffectiveMO,
  title={Effective metastability of Halpern iterates in CAT(0) spaces},
  author={Ulrich Kohlenbach and Laurentiu Leustean},
  journal={arXiv: Functional Analysis},
  year={2011}
}
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42 Citations
Highly Influential Citations
2
Background Citations
16
Methods Citations
15
Results Citations
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42 Citations

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Using proof-theoretical techniques, a proof by Hong-Kun Xu regarding a result of strong convergence for the Halpern type proximal point algorithm is analyzed and a rate of metastability and also of asymptotic regularity for the iteration are obtained.

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Addendum to “Effective metastability of Halpern iterates in CAT(0) spaces” [Adv. Math. 231 (5) (2012) 2526–2556]

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On the computational content of convergence proofs via Banach limits

A logical metatheorem guaranteeing the extractability of highly uniform rates of metastability under the stronger condition of the uniform smoothness of X is designed, combined with the method of eliminating Banach limits, which yields a full quantitative analysis of the proof by Shioji and Takahashi.

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A logical metatheorem guaranteeing the extractability of highly uniform rates of metastability under the stronger condition of the uniform smoothness of X is designed, combined with the method of eliminating Banach limits, which yields a full quantitative analysis of the proof by Shioji and Takahashi.

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