{"id":"https://openalex.org/W2309229136","doi":"https://doi.org/10.1007/s10957-016-0979-x","title":"On Some Basic Results Related to Affine Functions on Riemannian Manifolds","display_name":"On Some Basic Results Related to Affine Functions on Riemannian Manifolds","publication_year":2016,"publication_date":"2016-07-18","ids":{"openalex":"https://openalex.org/W2309229136","doi":"https://doi.org/10.1007/s10957-016-0979-x","mag":"2309229136"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-016-0979-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-016-0979-x","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103092956","display_name":"Xiangmei Wang","orcid":"https://orcid.org/0000-0001-7296-8588"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangmei Wang","raw_affiliation_strings":["College of Science, Guizhou University, Guiyang, 550025, People\u2019s Republic of China","College of Science, Guizhou University, Guiyang, 550025, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Guizhou University, Guiyang, 550025, People\u2019s Republic of China","institution_ids":["https://openalex.org/I178232147"]},{"raw_affiliation_string":"College of Science, Guizhou University, Guiyang, 550025, People's Republic of China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100424917","display_name":"Chong Li","orcid":"https://orcid.org/0000-0001-7097-4220"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chong Li","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People\u2019s Republic of China","School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People's Republic of China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050520268","display_name":"Jen\u2010Chih Yao","orcid":"https://orcid.org/0000-0001-9041-3375"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jen-Chih Yao","raw_affiliation_strings":["Center for General Education, China Medical University, Taichung, 40402, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for General Education, China Medical University, Taichung, 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100424917"],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.3261,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.64734282,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"170","issue":"3","first_page":"783","last_page":"803"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8267406225204468},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7454593777656555},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.671238899230957},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6272531151771545},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.5832302570343018},{"id":"https://openalex.org/keywords/pseudoconvex-function","display_name":"Pseudoconvex function","score":0.5121629238128662},{"id":"https://openalex.org/keywords/assertion","display_name":"Assertion","score":0.501060962677002},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.46886616945266724},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4516073167324066},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42912423610687256},{"id":"https://openalex.org/keywords/proposition","display_name":"Proposition","score":0.4209984540939331},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3490760326385498},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2102724015712738},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.20802080631256104},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14650461077690125},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.13780620694160461},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07614302635192871}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8267406225204468},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7454593777656555},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.671238899230957},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6272531151771545},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.5832302570343018},{"id":"https://openalex.org/C118888059","wikidata":"https://www.wikidata.org/wiki/Q7254692","display_name":"Pseudoconvex function","level":5,"score":0.5121629238128662},{"id":"https://openalex.org/C40422974","wikidata":"https://www.wikidata.org/wiki/Q741248","display_name":"Assertion","level":2,"score":0.501060962677002},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.46886616945266724},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4516073167324066},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42912423610687256},{"id":"https://openalex.org/C2777152325","wikidata":"https://www.wikidata.org/wiki/Q108163","display_name":"Proposition","level":2,"score":0.4209984540939331},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3490760326385498},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2102724015712738},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.20802080631256104},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14650461077690125},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.13780620694160461},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07614302635192871},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-016-0979-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-016-0979-x","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0979-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-016-0979-x","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3128121057","display_name":null,"funder_award_id":"11571308, 11371325","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W112853844","https://openalex.org/W1572143211","https://openalex.org/W1983057379","https://openalex.org/W1984826475","https://openalex.org/W2011987913","https://openalex.org/W2046845960","https://openalex.org/W2049830000","https://openalex.org/W2058655938","https://openalex.org/W2071569531","https://openalex.org/W2078885283","https://openalex.org/W2082584863","https://openalex.org/W2097607403","https://openalex.org/W2134086356","https://openalex.org/W2331155048","https://openalex.org/W2573028792","https://openalex.org/W2962777248","https://openalex.org/W3038420293","https://openalex.org/W3040283615","https://openalex.org/W3129186208","https://openalex.org/W4206033904","https://openalex.org/W4235476591","https://openalex.org/W4246883249","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2587222766","https://openalex.org/W1981142672","https://openalex.org/W4288083173","https://openalex.org/W4398758929","https://openalex.org/W4390176194","https://openalex.org/W2066180314","https://openalex.org/W4248569606","https://openalex.org/W2364963568","https://openalex.org/W2393350255","https://openalex.org/W257189624"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
