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In this paper, we consider a problem of investigating the dependence of $$|B[P\\circ\\sigma](z)-\\alpha B[P\\circ\\rho](z)+\\beta\\{(\\frac{R+k}{k+r})^{n}-|\\alpha|\\}B[P\\circ\\rho](z)| $$ on the maximum and minimum modulus of $|P(z)|$ on $|z|=k$ for arbitrary real or complex numbers $\\alpha,\\beta\\in\\mathbb{C}$ with $|\\alpha|\\leq 1,|\\beta|\\leq 1,R>r\\geq k,$ $\\sigma(z)=Rz,$ $\\rho(z)=rz$ and establish certain sharp ","authors_text":"N. A. Rather, Suhail Gulzar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-03-30T05:01:38Z","title":"On an operator preserving inequalities between polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0067","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d690e0e17b1a8597df07de0f10f2d2624d816ba426e08f03ccf8cf88cb2273bf","target":"record","created_at":"2026-05-18T03:29:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dcf323062c23bf6f3ca526b6850ecc48efb62a5bc96d3f581976f4342cd5388e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2013-03-30T05:01:38Z","title_canon_sha256":"ee2618aefc9e057fbfdc5229a67e87597cc9df04d35c494edca06ee53cc5c5e5"},"schema_version":"1.0","source":{"id":"1304.0067","kind":"arxiv","version":1}},"canonical_sha256":"ee4f03b1eeb25c67bff58dcd1f5b18e6259deac6ab530d24dfe71b491b10141b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee4f03b1eeb25c67bff58dcd1f5b18e6259deac6ab530d24dfe71b491b10141b","first_computed_at":"2026-05-18T03:29:26.128963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:26.128963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"19hIVOz7JA00HhDheRXkDry1B6dA/+j+XZdmBCE72pGf9ygbmpwdmOLV6jNVUXpCUgzHZ7fNvCaQqYcAuufSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:26.129939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d690e0e17b1a8597df07de0f10f2d2624d816ba426e08f03ccf8cf88cb2273bf","sha256:5a774971dd33be8c71eaa3a630cf22062f3baf8334b29498a6c4383028c9961d"],"state_sha256":"5c939e54622dfb4d6e52fbc73bc42c2cb1342ee0620ddb9a577ed06687c3dc6c"}