{"paper":{"title":"Sharing of a set of meromorphic functions and Montel's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Kuldeep Singh Charak, Virender Singh","submitted_at":"2015-09-21T07:18:48Z","abstract_excerpt":"In this paper we prove the result: Let $\\mathcal{F}$ be a family of meromorphic functions on a domain $\\Omega$ such that every pair of members of $\\mathcal{F}$ shares a set $S:=\\left\\{\\psi_1(z), \\psi_2(z), \\psi_3(z) \\right\\}$ in $\\Omega$, where $\\psi_j(z), \\ j=1,2,3$ is meromorphic in $\\Omega.$ If for every $f\\in \\mathcal{F}$, $f(z_0)\\neq \\psi_i (z_0)$ whenever $\\psi_i(z_0)=\\psi_j(z_0)$ for $i,j\\in \\left\\{1,2,3 \\right\\}(i\\neq j)$ and $z_0\\in \\Omega ,$ then $\\mathcal{F}$ is normal in $\\Omega$. This result generalizes a result of M.Fang and W.Hong [Some results on normal family of meromorphic fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06128","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}