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

P. de T. Firmino; Laurenţiu Leuştean

doi:10.4171/pm/2148

July 30, 2025Portugaliae MathematicaOpen Access

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

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Key Points

The study calculates rates of asymptotic regularity for generalized Krasnoselskii-Mann iterations.
It reveals that certain parameter sequences yield quadratic rates of convergence.
Proof mining methods are employed to analyze nonexpansive mappings in uniformly convex spaces.
The findings contribute to understanding iterative methods in functional analysis.

Implication

Proof mining computes rates of asymptotic regularity for generalized Krasnoselskii-Mann iterations, indicating significant findings.

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→ X in a uniformly convex normed space X . For special choices of the parameter sequences, we obtain quadratic rates.

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Cite This Study

Firmino et al. (2025) studied this question.

synapsesocial.com/papers/68c1a12d54b1d3bfb60dc44e https://doi.org/10.4171/pm/2148

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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