Quantitative asymptotic regularity and $T$-asymptotic regularity for the inexact generalized Halpern iteration

Nicoleta Dumitru; Laurentiu Leustean

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arXiv · 2603.17105

Quantitative asymptotic regularity and $T$-asymptotic regularity for the inexact generalized Halpern iteration

Nicoleta Dumitru·Laurentiu Leustean

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Abstract

We apply proof mining techniques to obtain quantitative and qualitative results on asymptotic and T-asymptotic regularity for the inexact generalized Halpern iteration, a viscosity-type extension of an iteration recently studied by Kanzow and Shehu. Specializing our results to the Kanzow-Shehu iteration and the sequential averaging method (SAM) yields analogous results for these iterations. Furthermore, we compute rates of (T-)asymptotic regularity for particular choices of the parameter sequences, and for one of them, we obtain linear rates as an application of a lemma due to Sabach and Shtern.

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Nicoleta Dumitru, Laurentiu Leustean. 2026-03-17. Quantitative asymptotic regularity and $T$-asymptotic regularity for the inexact generalized Halpern iteration. https://arxiv.org/abs/2603.17105

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