Pith Number

pith:LITY4DUY

pith:2026:LITY4DUYHBO3ZM232WL3HPFWJN

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Petrov type extension for multivalued contraction mappings

Hakan Sahin, Ishak ALtun, Mustafa Aslantas

Multivalued mappings satisfying a new three-point perimeter contraction condition have fixed points in complete metric spaces when they form triangles.

arxiv:2605.13358 v1 · 2026-05-13 · math.FA

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\pithnumber{LITY4DUYHBO3ZM232WL3HPFWJN}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

Using the new concept of multivalued λ-contracting perimeters of triangles and the property of forming a triangle, we present some fixed point results for multivalued mappings.

C2weakest assumption

That a mapping satisfying the multivalued λ-contracting perimeters of triangles condition together with the triangle-forming property guarantees a fixed point in a complete metric space.

C3one line summary

The paper defines multivalued λ-contracting perimeters of triangles and the property of forming a triangle to prove fixed point theorems for multivalued mappings.

References

21 extracted · 21 resolved · 0 Pith anchors

[1] H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology Appl., 159 (14) (2012), 3234-3242 2012

[2] Banach, Sur les op´ erations dans les ensembles abstraits et leur application aux ´ equations int´ egrales, Fund 1922

[3] A. Bera, L. K. Dey, A. Petru¸ sel and A. Chanda, Best proximity results forp-proximal contractions on topological spaces, Carpathian J. Math., 39 (3) (2023), 621-632 2023

[4] V. Berinde, A. Petru¸ sel and I. A. Rus, Remarks on the terminology of the mappings in fixed point iterative methods in metric spaces, Fixed Point Theory, 24 (2) (2023), 525-540 2023

[5] D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Am. Math. Soc., 20 (1969), 458-464 1969

Receipt and verification

First computed	2026-05-18T02:44:48.186235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a278e0e98385dbcb35bd597b3bcb64b4512ca574ddf83b2967453ecb75941a8

Aliases

arxiv: 2605.13358 · arxiv_version: 2605.13358v1 · doi: 10.48550/arxiv.2605.13358 · pith_short_12: LITY4DUYHBO3 · pith_short_16: LITY4DUYHBO3ZM23 · pith_short_8: LITY4DUY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LITY4DUYHBO3ZM232WL3HPFWJN \
  | 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: 5a278e0e98385dbcb35bd597b3bcb64b4512ca574ddf83b2967453ecb75941a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f713b9a81496518c01c0d6c9d4533b078779fab1220800cffbc7228d4a96102c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-13T11:18:52Z",
    "title_canon_sha256": "477feb4cc2a3cc1f07e93eddb657856b0a18927ddb86e864932510a75bd108b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13358",
    "kind": "arxiv",
    "version": 1
  }
}