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Rather, Suhail Gulzar","submitted_at":"2013-02-28T03:22:19Z","abstract_excerpt":"Let $ P(z) $ be a polynomial of degree $ n $ having all zeros in $|z|\\leq k$ where $k\\leq 1,$ then it was proved by Dewan \\textit{et al} that for every real or complex number $\\alpha$ with $|\\alpha|\\geq k$ and each $r\\geq 0$\n  $$ n(|\\alpha|-k)\\left\\{\\int\\limits_{0}^{2\\pi}\\left|P\\left(e^{i\\theta}\\right)\\right|^r d\\theta\\right\\}^{\\frac{1}{r}}\\leq\\left\\{\\int\\limits_{0}^{2\\pi}\\left|1+ke^{i\\theta}\\right|^r d\\theta\\right\\}^{\\frac{1}{r}}\\underset{|z|=1}{Max}|D_\\alpha P(z)|. $$\n  \\indent In this paper, we shall present a refinement and generalization of above result and also extend it to the class of "},"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":"1302.7066","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-02-28T03:22:19Z","cross_cats_sorted":[],"title_canon_sha256":"c3de4d697760dcde9f0399dd26cf7a7de3259c91f5fb6918f6c82c999a9d252c","abstract_canon_sha256":"046479d584226790ae61ee1c9cf93d3fe580fe5a158b7771476c8fea3033cdc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:15.493880Z","signature_b64":"dHUipLgvIyLay/6BRP/pbWf0CvshDqoUbEop9NRE1l462kgEf4WwUeNHvvy1U1gQiTG2V08SCEx05JE4gcwQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d5943468c1f50baeb7098a4626258c9f80630aa01148b2b36858831c0a0fc78","last_reissued_at":"2026-05-18T03:29:15.493402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:15.493402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral mean estimates for the polar derivative of a polynomial","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"N. 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