{
  "abstract": "We study an implicit iteration for approximating common fixed points of strongly continuous semigroups on closed convex subsets of real Banach spaces. Under a stepwise Lipschitz restriction and hemi-contractivity relative to the common fixed point set, we establish well-definedness and Fej% ér monotonicity of the iteration. In reflexive Banach spaces satisfying Opial's condition, we obtain a sufficient condition for weak convergence based on a normalized residual estimate, uniform continuity at zero along the generated sequence, and demiclosedness at fixed positive times. In general real Banach spaces, we prove strong convergence under a time-dependent directional contraction condition and a divergence condition coupling the iteration weights with the contraction strength. A linear example shows that vanishing time steps and a divergent sum of iteration weights alone do not ensure convergence to a common fixed point. A nonlinear planar evolution semigroup illustrates the applicability of the strong convergence theorem beyond the nonexpansive class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.25799",
  "author_total": 1,
  "authors": [
    {
      "name": "Ferit Gürbüz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mtxhxzyrehx2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25799",
  "fulltext_url": null,
  "id": "2mtxhxzyrehx2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25799",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7165903057",
  "pdf_url": "https://arxiv.org/pdf/2606.25799",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mtxhxzyrehx2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2606.25799",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25799"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weak and Strong Convergence of an Implicit Iteration for Hemi-Contractive Semigroups in Banach Spaces",
  "title_text": "Weak and Strong Convergence of an Implicit Iteration for Hemi-Contractive Semigroups in Banach Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2mtxhxzyrehx2",
  "venue": "arXiv",
  "versions": []
}