{"id":"https://openalex.org/W1987626153","doi":"https://doi.org/10.1155/2012/931656","title":"On Upper and Lower -Continuous Multifunctions","display_name":"On Upper and Lower -Continuous Multifunctions","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1987626153","doi":"https://doi.org/10.1155/2012/931656","mag":"1987626153"},"language":"en","primary_location":{"id":"doi:10.1155/2012/931656","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/931656","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/931656.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/931656.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044537734","display_name":"Chawalit Boonpok","orcid":"https://orcid.org/0000-0002-7933-6396"},"institutions":[{"id":"https://openalex.org/I123096312","display_name":"Mahasarakham University","ror":"https://ror.org/0453j3c58","country_code":"TH","type":"education","lineage":["https://openalex.org/I123096312"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Chawalit Boonpok","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand","Department of mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand","institution_ids":["https://openalex.org/I123096312"]},{"raw_affiliation_string":"Department of mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044537734"],"corresponding_institution_ids":["https://openalex.org/I123096312"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.9994,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86626087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9574730396270752},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6277034282684326},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44542351365089417},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3623676598072052},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23430278897285461}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9574730396270752},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6277034282684326},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44542351365089417},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3623676598072052},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23430278897285461},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/931656","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/931656","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/931656.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a957e7d1bfd44f18a3f117b37fadac6a","is_oa":true,"landing_page_url":"https://doaj.org/article/a957e7d1bfd44f18a3f117b37fadac6a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2012/931656","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/931656","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2012/931656","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/931656","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/931656.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324290","display_name":"Mahasarakham University","ror":"https://ror.org/0453j3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1987626153.pdf","grobid_xml":"https://content.openalex.org/works/W1987626153.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W43501056","https://openalex.org/W76958545","https://openalex.org/W80194025","https://openalex.org/W145647622","https://openalex.org/W1867024875","https://openalex.org/W1977953273","https://openalex.org/W1992117499","https://openalex.org/W2016791671","https://openalex.org/W2017243498","https://openalex.org/W2021513740","https://openalex.org/W2037276849","https://openalex.org/W2053750445","https://openalex.org/W2056549090","https://openalex.org/W2057154512","https://openalex.org/W2084371632","https://openalex.org/W2087426551","https://openalex.org/W2092266125","https://openalex.org/W2138139093","https://openalex.org/W2156311117","https://openalex.org/W2282005585","https://openalex.org/W3086344570","https://openalex.org/W4241966728","https://openalex.org/W4249939961","https://openalex.org/W4253611677","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"A":[0],"new":[1],"class":[2],"of":[3],"multifunctions,":[4,9],"called":[5],"upper":[6,21,30],"(lower)":[7,22,31],"-continuous":[8,23,32],"has":[10],"been":[11],"defined":[12],"and":[13,17,34],"studied.":[14],"Some":[15],"characterizations":[16],"several":[18],"properties":[19],"concerning":[20],"multifunctions":[24,33],"are":[25,38],"obtained.":[26],"The":[27],"relationships":[28],"between":[29],"some":[35],"known":[36],"concepts":[37],"also":[39],"discussed.":[40]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}