Rates of ($T$-)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration

Paulo Firmino; Laurenţiu Leuştean

doi:10.4171/pm/2148

JournalspmOnline First

Rates of ( $T$ -)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration

Paulo Firmino
Universidade de Lisboa, Portugal
ORCID
Laurenţiu Leuştean
University of Bucharest, Romania; Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania; Institute for Logic and Data Science, Bucharest, Romania
ORCID

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Abstract

In this paper, we use proof mining methods to compute rates of ( $T$ -)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration associated to a nonexpansive mapping $T : X \to X$ in a uniformly convex normed space $X$ . For special choices of the parameter sequences, we obtain quadratic rates.

Cite this article

Paulo Firmino, Laurenţiu Leuştean, Rates of ( $T$ -)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration. Port. Math. (2025), published online first

DOI 10.4171/PM/2148