{"id":"https://openalex.org/W126412899","doi":"https://doi.org/10.1007/978-3-642-22833-9_50","title":"The (h, \u03d5)\u2013Generalized Second-Order Directional Derivative in Banach Space","display_name":"The (h, \u03d5)\u2013Generalized Second-Order Directional Derivative in Banach Space","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W126412899","doi":"https://doi.org/10.1007/978-3-642-22833-9_50","mag":"126412899"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-22833-9_50","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-22833-9_50","pdf_url":null,"source":{"id":"https://openalex.org/S4210208846","display_name":"Advances in intelligent and soft computing","issn_l":"1867-5662","issn":["1867-5662","1867-5670"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent and Soft Computing","raw_type":"book-chapter"},"type":"book-chapter","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/A5100634093","display_name":"Wenjuan Chen","orcid":"https://orcid.org/0000-0001-6633-6664"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjuan Chen","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, No.6 Middle School Linyi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, No.6 Middle School Linyi, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100936727","display_name":"Cao-zong Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Caozong Cheng","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051565137","display_name":"Caiyun Jin","orcid":"https://orcid.org/0000-0002-2740-9346"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Caiyun Jin","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04855086,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"411","last_page":"418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9781000018119812,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9781000018119812,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9681000113487244,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9517999887466431,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5326186418533325},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5079334378242493},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4972389042377472},{"id":"https://openalex.org/keywords/infinite-dimensional-vector-function","display_name":"Infinite-dimensional vector function","score":0.47400224208831787},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4287834167480469},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4234570860862732},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.41405269503593445},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3487839698791504},{"id":"https://openalex.org/keywords/eberlein\u2013\u0161mulian-theorem","display_name":"Eberlein\u2013\u0160mulian theorem","score":0.3220319151878357},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2881559729576111},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24432778358459473},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.14211836457252502},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.12614011764526367}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5326186418533325},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5079334378242493},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4972389042377472},{"id":"https://openalex.org/C80739010","wikidata":"https://www.wikidata.org/wiki/Q6029720","display_name":"Infinite-dimensional vector function","level":5,"score":0.47400224208831787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4287834167480469},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4234570860862732},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.41405269503593445},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3487839698791504},{"id":"https://openalex.org/C184908153","wikidata":"https://www.wikidata.org/wiki/Q2226650","display_name":"Eberlein\u2013\u0160mulian theorem","level":4,"score":0.3220319151878357},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2881559729576111},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24432778358459473},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.14211836457252502},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.12614011764526367},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-22833-9_50","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-22833-9_50","pdf_url":null,"source":{"id":"https://openalex.org/S4210208846","display_name":"Advances in intelligent and soft computing","issn_l":"1867-5662","issn":["1867-5662","1867-5670"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent and Soft Computing","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1590012787","https://openalex.org/W1986606318","https://openalex.org/W2115566940","https://openalex.org/W2383730205"],"related_works":["https://openalex.org/W1970606660","https://openalex.org/W4301239495","https://openalex.org/W3181765342","https://openalex.org/W2357156800","https://openalex.org/W40430404","https://openalex.org/W2625002492","https://openalex.org/W2754689669","https://openalex.org/W2039112049","https://openalex.org/W2114637546","https://openalex.org/W2024846128"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}