Pith Number

pith:NHM7D5EG

pith:2026:NHM7D5EG7H6QKS3YINPJDIFTZE

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On fixed point results in metric spaces for large triangle-perimeter contractions

Ovidiu Popescu

Fixed point theorem for large triangle-perimeter contractions holds only under an auxiliary condition.

arxiv:2605.13147 v1 · 2026-05-13 · math.DS

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Given an additional condition, a fixed point result for large triangle-perimeter contractions holds.

C2weakest assumption

The auxiliary condition imposed on the large triangle-perimeter contraction that is required for the fixed point theorem to hold.

C3one line summary

Large triangle-perimeter contractions admit fixed points when an auxiliary condition is added, as shown by a counterexample to the prior claim and a new proof that covers a strictly larger class than Burton's or Petrov's theories.

References

8 extracted · 8 resolved · 0 Pith anchors

[1] Banach, Sur les op´ erations dans les ensembles abstraits et leur application aux ´ equations int´ egrales, Fundamenta Mathematicae 3 (1922), 133-181 1922

[2] Burton, Integral equations, implicit functions, and fixed points 1996

[3] S. K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727–730 1972

[4] A. Dehici, M.B. Mesmouli, E. Karapinar, On the fixed points of large- Kannan contraction mappings and applications. Appl. Math.-E-Notes 2019, 19, 535–551. 9 2019

[5] Kannan, Some results on fixed point - II, Amer 1969

Receipt and verification

First computed	2026-05-18T03:08:57.249462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69d9f1f486f9fd054b78435e91a0b3c904458dbf76fd0949ef76ba80ebab0185

Aliases

arxiv: 2605.13147 · arxiv_version: 2605.13147v1 · doi: 10.48550/arxiv.2605.13147 · pith_short_12: NHM7D5EG7H6Q · pith_short_16: NHM7D5EG7H6QKS3Y · pith_short_8: NHM7D5EG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NHM7D5EG7H6QKS3YINPJDIFTZE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 69d9f1f486f9fd054b78435e91a0b3c904458dbf76fd0949ef76ba80ebab0185

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "903d8a0b4bd2ebb9f994937f45f15742bca314e7786837fe4b8d85f72d5bbe8b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-13T08:14:32Z",
    "title_canon_sha256": "252d2d40f6700ba12c1811a6951c43a7671b717fedbf95df6870146fc2b6a9f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13147",
    "kind": "arxiv",
    "version": 1
  }
}