{"paper":{"title":"On generalized Ces\\`aro stable functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"A. Swaminathan, Priyanka Sangal","submitted_at":"2017-05-11T11:25:02Z","abstract_excerpt":"The notion of Ces\\`aro stable function is generalized by introducing Ces\\`aro mean of type $(b-1;c)$ which give rise to a new concept of generalized Ces\\`aro stable function. As an application of generalized Ces\\`aro stable functions we also prove for a convex function of order $\\lambda\\in[1/2,1)$, its Ces\\`aro mean of type $(b-1;c)$ is close-to-convex of order $\\lambda$. Further two conjectures are also posed in the direction of generalized Ces\\`aro stable function. Some particular cases of these conjectures are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04112","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"}