{
  "abstract": "Solving fixed-point problems by reducing residual bounds is one of the central approaches in fixed-point iteration, and, in particular, the Halpern iteration is known to effectively reduce the residual. Recently, a new type of duality theorem has been discovered in the convex optimization and fixed-point problem literature and establish a certain symmetry in the convergence behavior of algorithms that are dual to each other. However, these duality theorems rely on a Lyapunov-style proof structure and mostly focus on Hilbert spaces. In this work, we first establish an M-duality theorem for Mann iterations with Lipschitz operators in general normed spaces, assuming only mild conditions on the coefficients of the iterations. Moreover, leveraging this M-duality, we derive new algorithms that attain a strictly smaller worst-case residual bound than that of the Halpern iteration, which was previously known as the state-of-the-art method in general normed spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08151",
  "author_total": 3,
  "authors": [
    {
      "name": "Jongmin Lee"
    },
    {
      "name": "Sangyeop Woo"
    },
    {
      "name": "Ernest K. Ryu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fhywkx7fcwm6t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08151",
  "fulltext_url": null,
  "id": "fhywkx7fcwm6t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08151",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7212027622",
  "pdf_url": "https://arxiv.org/pdf/2609.08151",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fhywkx7fcwm6t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08151",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08151"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "M-duality in fixed-point problems for general normed spaces",
  "title_text": "M-duality in fixed-point problems for general normed spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/fhywkx7fcwm6t",
  "venue": "arXiv",
  "versions": []
}