{"id":"https://openalex.org/W4412995704","doi":"https://doi.org/10.3390/axioms14080600","title":"Characterization of the Best Approximation and Establishment of the Best Proximity Point Theorems in Lorentz Spaces","display_name":"Characterization of the Best Approximation and Establishment of the Best Proximity Point Theorems in Lorentz Spaces","publication_year":2025,"publication_date":"2025-08-01","ids":{"openalex":"https://openalex.org/W4412995704","doi":"https://doi.org/10.3390/axioms14080600"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14080600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080600","pdf_url":"https://www.mdpi.com/2075-1680/14/8/600/pdf?version=1754459917","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/8/600/pdf?version=1754459917","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090556479","display_name":"Dezhou Kong","orcid":"https://orcid.org/0000-0001-8399-7763"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dezhou Kong","raw_affiliation_strings":["College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China"],"raw_orcid":"https://orcid.org/0000-0001-8399-7763","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","institution_ids":["https://openalex.org/I74485261"]},{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103167699","display_name":"Zhihao Xu","orcid":"https://orcid.org/0000-0002-4304-9061"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhihao Xu","raw_affiliation_strings":["College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","institution_ids":["https://openalex.org/I74485261"]},{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021959214","display_name":"Yun Wang","orcid":"https://orcid.org/0000-0001-5993-114X"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yun Wang","raw_affiliation_strings":["College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China"],"raw_orcid":"https://orcid.org/0000-0001-5993-114X","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","institution_ids":["https://openalex.org/I74485261"]},{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China","institution_ids":["https://openalex.org/I74485261"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101966878","display_name":"Li Sun","orcid":"https://orcid.org/0000-0002-3589-4898"},"institutions":[{"id":"https://openalex.org/I74485261","display_name":"Shandong Agricultural University","ror":"https://ror.org/02ke8fw32","country_code":"CN","type":"education","lineage":["https://openalex.org/I74485261"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li Sun","raw_affiliation_strings":["College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China"],"raw_orcid":"https://orcid.org/0000-0002-3589-4898","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai\u2019an 271018, China","institution_ids":["https://openalex.org/I74485261"]},{"raw_affiliation_string":"College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China","institution_ids":["https://openalex.org/I74485261"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101966878"],"corresponding_institution_ids":["https://openalex.org/I74485261"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24343195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"8","first_page":"600","last_page":"600"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9958000183105469,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/characterization","display_name":"Characterization (materials science)","score":0.8679994344711304},{"id":"https://openalex.org/keywords/lorentz-transformation","display_name":"Lorentz transformation","score":0.6845859885215759},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6033508777618408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.52821284532547},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4289277493953705},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3566333055496216},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2471546232700348},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12352526187896729},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09020376205444336},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.06014657020568848}],"concepts":[{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.8679994344711304},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.6845859885215759},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6033508777618408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.52821284532547},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4289277493953705},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3566333055496216},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2471546232700348},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12352526187896729},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09020376205444336},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.06014657020568848}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14080600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080600","pdf_url":"https://www.mdpi.com/2075-1680/14/8/600/pdf?version=1754459917","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a6673731e2cd499db0e0a61935544bf1","is_oa":true,"landing_page_url":"https://doaj.org/article/a6673731e2cd499db0e0a61935544bf1","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 8, p 600 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14080600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080600","pdf_url":"https://www.mdpi.com/2075-1680/14/8/600/pdf?version=1754459917","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3960398203","display_name":null,"funder_award_id":"ZR2022MA009","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G565492982","display_name":null,"funder_award_id":"71773067","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5777460465","display_name":null,"funder_award_id":"11871302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6210091655","display_name":null,"funder_award_id":"11871302","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412995704.pdf","grobid_xml":"https://content.openalex.org/works/W4412995704.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W328800714","https://openalex.org/W935814424","https://openalex.org/W1486515847","https://openalex.org/W1534337369","https://openalex.org/W1576423523","https://openalex.org/W1974414276","https://openalex.org/W1976131478","https://openalex.org/W1977774625","https://openalex.org/W1978706921","https://openalex.org/W1978792384","https://openalex.org/W1981222881","https://openalex.org/W1988461593","https://openalex.org/W1993974518","https://openalex.org/W2006380466","https://openalex.org/W2008696186","https://openalex.org/W2010043402","https://openalex.org/W2012206480","https://openalex.org/W2022535940","https://openalex.org/W2057927789","https://openalex.org/W2064008630","https://openalex.org/W2067894692","https://openalex.org/W2080863166","https://openalex.org/W2103679879","https://openalex.org/W2140975540","https://openalex.org/W2160026266","https://openalex.org/W2259693690","https://openalex.org/W2260723571","https://openalex.org/W2315698296","https://openalex.org/W2538045951","https://openalex.org/W2591355265","https://openalex.org/W2750824306","https://openalex.org/W2765459804","https://openalex.org/W2957843237","https://openalex.org/W2963683203","https://openalex.org/W2963823726","https://openalex.org/W2964118279","https://openalex.org/W3016310801","https://openalex.org/W4394578271","https://openalex.org/W4403186856","https://openalex.org/W4412641728","https://openalex.org/W6624547888","https://openalex.org/W6629801980","https://openalex.org/W6632250378"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3107994849","https://openalex.org/W4247143848","https://openalex.org/W2009883749","https://openalex.org/W2735573198","https://openalex.org/W29442446","https://openalex.org/W330727063","https://openalex.org/W2896904446","https://openalex.org/W1483407203","https://openalex.org/W4206825956"],"abstract_inverted_index":{"Since":[0],"the":[1,4,20,37,46,58,69,93,98,101,104,111,117,121,150,153],"monotonicity":[2,38,43,67,119],"of":[3,45,68,103,152],"best":[5,21,105,127],"approximant":[6],"is":[7,97],"crucial":[8],"to":[9,89],"establish":[10],"partial":[11,112,156],"ordering":[12,113,157],"methods,":[13],"in":[14,23,31,52,80,139,149],"this":[15],"paper,":[16],"we,":[17],"respectively,":[18,78],"characterize":[19],"approximants":[22],"Banach":[24,54],"function":[25,55],"spaces":[26,29,56,84],"and":[27,63,74,123,136,144,155],"Lorentz":[28,83],"\u0393p,w,":[30],"which":[32,96],"we":[33],"especially":[34],"focus":[35],"on":[36,116],"characterizations.":[39],"We":[40],"first":[41],"study":[42],"characterizations":[44],"metric":[47,70],"projection":[48,71],"operator":[49],"onto":[50,72],"sublattices":[51,75],"general":[53],"by":[57,109],"property":[59],"Hg.":[60],"The":[61,82],"sufficient":[62],"necessary":[64],"conditions":[65,138],"for":[66,100,126],"cones":[73],"are":[76,86,130],"then,":[77],"established":[79],"\u0393p,w.":[81,140],"\u0393p,w":[85],"also":[87],"shown":[88],"be":[90],"reflexive":[91],"under":[92],"condition":[94],"RBp,":[95],"basis":[99],"existence":[102],"approximant.":[106],"As":[107],"applications,":[108],"establishing":[110],"methods":[114],"based":[115],"obtained":[118],"characterizations,":[120],"solvability":[122],"approximation":[124,154],"theorems":[125],"proximity":[128],"points":[129],"deduced":[131],"without":[132],"imposing":[133],"any":[134],"contractive":[135],"compact":[137],"Our":[141],"results":[142,148],"extend":[143],"improve":[145],"many":[146],"previous":[147],"field":[151],"theory.":[158]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
