A Banach-Type Fixed Point Theorem via Discrepancy Functionals

[2608.14612] A Banach-Type Fixed Point Theorem via Discrepancy Functionals Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > General Mathematics arXiv:2608.14612 (math) [Submitted on 9 Jul 2026] Title: A Banach-Type Fixed Point Theorem via Discrepancy Functionals Authors: Hallowed Olaoluwa View a PDF of the paper titled A Banach-Type Fixed Point Theorem via Discrepancy Functionals, by Hallowed Olaoluwa View PDF HTML (experimental) Abstract: In this paper we establish a Banach-type fixed point theorem for mappings that contract a general nonnegative functional rather than a metric. The principal assumption is that the functional dominates the underlying metric through a simple lower bound, together with a compatibility condition at limits. Our result provides a common framework that recovers recent fixed point theorems in perturbed metric spaces and for polynomial contractions as particular cases, while showing that neither symmetry nor the triangle inequality is essential for the contraction argument. Consequently, the contractive quantity may be interpreted as a general discrepancy or divergence measure rather than a metric. The results highlight that the essential ingredient behind Banach's contraction principle is not the metric structure itself, but the ability of the contracted functional to control the geometry of the underlying space. This perspective provides a simple and flexible framework for obtaining fixed point results for broad classes of non-metrical contractive quantities. Comments: 6 pages Subjects: General Mathematics (math.GM) Cite as: arXiv:2608.14612 [math.GM] (or arXiv:2608.14612v1 [math.GM] for this version) https://doi.org/10.48550/arXiv.2608.14612 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hallowed Olaoluwa [ view email ] [v1] Thu, 9 Jul 2026 17:25:27 UTC (6 KB) Full-text links: Access Paper: View a PDF of the paper titled A Banach-Type Fixed Point Theorem via Discrepancy Functionals, by Hallowed Olaoluwa View PDF HTML (experimental) TeX Source view license Current browse context: math.GM < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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