{"corpus_id":40735491,"paper_sha":"e2cc60578c175a6b2f208ec1b8c0a0f31b07224e","doi":"10.1155/S0161171299227652","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2095216280,"dblp_id":null,"acl_id":null,"title":"Sufficiency for Gaussian hypergeometric functions to be uniformly convex","year":1999,"publication_date":null,"venue":"","journal":{"name":"International Journal of Mathematics and Mathematical Sciences","pages":"765-773","volume":"22"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":13,"citation_count":13,"influential_citation_count":2,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z)=zF(a,b;c;z)*f(z). In this paper the authors identify two subfamilies of analytic functions ℱ1 and ℱ2 and obtain conditions on the parameters a,b,c such that f∈ℱ1 implies Ia,b;c(f)∈ℱ2.","claims":[{"public_id":"cl_7faf8083e3d022ab338fb2d0dd11f876","status":"active","text":"A convolution operator defined using the Gaussian hypergeometric function F(a,b;c;z) is used to establish sufficiency criteria for uniform convexity.","confidence":0.9,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_7faf8083e3d022ab338fb2d0dd11f876"},{"public_id":"cl_49c0edd4e7f6b8bcec504fb04f3ec8b3","status":"active","text":"Conditions on the parameters a, b, and c are identified that ensure functions in the subfamily ℱ1 are mapped by Iₐ,ᵦ;𝚌 into the subfamily ℱ2.","confidence":0.96,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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