Pith Number

pith:MYSCFHJZ

pith:2025:MYSCFHJZTWVK5IY6KIIUZIH7QQ

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Semi-discrete moduli of smoothness and their applications in one- and two- sided error estimates

Danilo Costarelli, Donato Lavella

A new semi-discrete modulus of smoothness produces sharper one- and two-sided error estimates for pointwise linear operators than classical averaged moduli.

arxiv:2506.10723 v4 · 2025-06-12 · math.NA · cs.NA · math.FA

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Claims

C1strongest claim

By the definition of semi-discrete moduli of smoothness here proposed, we derive sharper estimates than those that can be achieved by the classical averaged moduli of smoothness (τ-moduli). Furthermore, a Rathore-type theorem is established, and a new notion of K-functional is also introduced showing its equivalence with the semi-discrete modulus of smoothness and its realization.

C2weakest assumption

The regularization and approximation properties of certain Steklov integrals introduced by Sendov and Popov in 1983, together with the non-restrictive assumptions placed on the pointwise linear operators, are invoked to establish the error estimates and equivalences.

C3one line summary

Introduces semi-discrete moduli of smoothness for sharper one- and two-sided error estimates in approximation by pointwise linear operators, with a new equivalent K-functional.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-28T02:04:41.082707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6624229d399daaaea31e52114ca0ff8406c8a5ad4551b8201d619399b49d74e8

Aliases

arxiv: 2506.10723 · arxiv_version: 2506.10723v4 · doi: 10.48550/arxiv.2506.10723 · pith_short_12: MYSCFHJZTWVK · pith_short_16: MYSCFHJZTWVK5IY6 · pith_short_8: MYSCFHJZ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MYSCFHJZTWVK5IY6KIIUZIH7QQ \
  | 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: 6624229d399daaaea31e52114ca0ff8406c8a5ad4551b8201d619399b49d74e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fbc1eea3c34a84081d138377a3e9bc00c568ab6c210e2e1b97354d7fcad7110",
    "cross_cats_sorted": [
      "cs.NA",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-06-12T14:12:19Z",
    "title_canon_sha256": "f508e3d367c269e354099476a4a08203873b87df29d9b4e6c241d7ddcd584693"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.10723",
    "kind": "arxiv",
    "version": 4
  }
}