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We generalize some inequalities including Euclidean operator radius of two operators to those involving $w_p$. Further we obtain some lower and upper bounds for $w_p$. Our main result states that if $f$ and $g$ are nonnegative continuous functions on $\\left[ 0,\\infty \\right) $ satisfying $f\\left( t\\right) g\\left(t\\right) =t$ for all "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.00083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-31T08:41:32Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"5675a10085a0764f1826959f537228b719e910c4613dcb07e9e8a4d8e21cdfa8","abstract_canon_sha256":"2db37020bad0bd6a70cafa115b4d5561d009d20d229514e57f60ac339ffce24b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:12.829849Z","signature_b64":"8b6EcvBTTjLAk+/JiLn3OakUToJzXxAWpYdSN3xAf6e6IuSaKZZre8vwHDwvF9hpw9N+jgvdfKmvnmei3y+zBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b850a830206378c7d90897803cd444fb40828022aa54c4b8e0f3bae7ca5ec07","last_reissued_at":"2026-05-18T02:28:12.829350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:12.829350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension of Euclidean operator radius inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"K. 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