{"id":"https://openalex.org/W4386781996","doi":"https://doi.org/10.3390/sym15091762","title":"Fixed Point Results via Orthogonal (\u03b1\u2212y\u2212G)-Contraction in Orthogonal Complete Metric Space","display_name":"Fixed Point Results via Orthogonal (\u03b1\u2212y\u2212G)-Contraction in Orthogonal Complete Metric Space","publication_year":2023,"publication_date":"2023-09-14","ids":{"openalex":"https://openalex.org/W4386781996","doi":"https://doi.org/10.3390/sym15091762"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091762","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091762","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1762/pdf?version=1694703523","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/9/1762/pdf?version=1694703523","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100774439","display_name":"Xiaolan Liu","orcid":"https://orcid.org/0000-0001-8904-6782"},"institutions":[{"id":"https://openalex.org/I64852412","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23","country_code":"CN","type":"education","lineage":["https://openalex.org/I64852412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaolan Liu","raw_affiliation_strings":["College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China","Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong 643000, China","South Sichuan Center for Applied Mathematics, Zigong 643000, China"],"raw_orcid":"https://orcid.org/0000-0001-8904-6782","affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China","institution_ids":["https://openalex.org/I64852412"]},{"raw_affiliation_string":"Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong 643000, China","institution_ids":["https://openalex.org/I64852412"]},{"raw_affiliation_string":"South Sichuan Center for Applied Mathematics, Zigong 643000, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083989384","display_name":"Gunasekaran Nallaselli","orcid":"https://orcid.org/0000-0002-2127-0734"},"institutions":[{"id":"https://openalex.org/I145286018","display_name":"SRM Institute of Science and Technology","ror":"https://ror.org/050113w36","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gunasekaran Nallaselli","raw_affiliation_strings":["Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India","institution_ids":["https://openalex.org/I145286018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090638387","display_name":"Absar Ul Haq","orcid":"https://orcid.org/0000-0002-3090-1294"},"institutions":[{"id":"https://openalex.org/I142732210","display_name":"University of Engineering and Technology Lahore","ror":"https://ror.org/0051w2v06","country_code":"PK","type":"education","lineage":["https://openalex.org/I142732210"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Absar Haq","raw_affiliation_strings":["Department of Natural Sciences and Humanities, University of Engineering and Technology (Narowal Campus), Lahore 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Natural Sciences and Humanities, University of Engineering and Technology (Narowal Campus), Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I142732210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014240219","display_name":"Arul Joseph Gnanaprakasam","orcid":"https://orcid.org/0000-0001-6346-605X"},"institutions":[{"id":"https://openalex.org/I145286018","display_name":"SRM Institute of Science and Technology","ror":"https://ror.org/050113w36","country_code":"IN","type":"education","lineage":["https://openalex.org/I145286018"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Arul Gnanaprakasam","raw_affiliation_strings":["Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"],"raw_orcid":"https://orcid.org/0000-0001-6346-605X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India","institution_ids":["https://openalex.org/I145286018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080553002","display_name":"Imran Abbas Baloch","orcid":"https://orcid.org/0000-0001-8941-2527"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Imran Baloch","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan","Higher Education Department, Government Graduate College for Boys Gulberg, Lahore 54600, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-8941-2527","affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan","institution_ids":["https://openalex.org/I43879129"]},{"raw_affiliation_string":"Higher Education Department, Government Graduate College for Boys Gulberg, Lahore 54600, Pakistan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5014240219","https://openalex.org/A5080553002"],"corresponding_institution_ids":["https://openalex.org/I145286018","https://openalex.org/I43879129"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.194574,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"9","first_page":"1762","last_page":"1762"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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":0.7677080631256104},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6554241180419922},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5495301485061646},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.47457459568977356},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.46576738357543945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44351333379745483},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43658381700515747}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7677080631256104},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6554241180419922},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5495301485061646},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.47457459568977356},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.46576738357543945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44351333379745483},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43658381700515747},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym15091762","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091762","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1762/pdf?version=1694703523","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1431671fcaa34747b15c83b8767979b1","is_oa":false,"landing_page_url":"https://doaj.org/article/1431671fcaa34747b15c83b8767979b1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 9, p 1762 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15091762","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091762","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1762/pdf?version=1694703523","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1746295939","display_name":null,"funder_award_id":"Y2022190","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G3168117220","display_name":null,"funder_award_id":"cx2021150","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G7234678836","display_name":null,"funder_award_id":"2023NSFSC1299","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G7311558159","display_name":null,"funder_award_id":"11872043","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G8258946623","display_name":null,"funder_award_id":"2022RC04","funder_id":"https://openalex.org/F4320322947","funder_display_name":"Sichuan University of Science and Engineering"},{"id":"https://openalex.org/G8857284349","display_name":null,"funder_award_id":"11872043","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"},{"id":"https://openalex.org/F4320322947","display_name":"Sichuan University of Science and Engineering","ror":"https://ror.org/053fzma23"},{"id":"https://openalex.org/F4320322990","display_name":"Sichuan University","ror":"https://ror.org/011ashp19"},{"id":"https://openalex.org/F4320326275","display_name":"Higher Education Commision, Pakistan","ror":null},{"id":"https://openalex.org/F4320329861","display_name":"Natural Science Foundation of Sichuan Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386781996.pdf","grobid_xml":"https://content.openalex.org/works/W4386781996.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1458771408","https://openalex.org/W1970229082","https://openalex.org/W1980761056","https://openalex.org/W2033682671","https://openalex.org/W2094611044","https://openalex.org/W2123660171","https://openalex.org/W2153432132","https://openalex.org/W2323245002","https://openalex.org/W2611928757","https://openalex.org/W2614373420","https://openalex.org/W2735530910","https://openalex.org/W2743088623","https://openalex.org/W2985933319","https://openalex.org/W4214876059","https://openalex.org/W4242933910","https://openalex.org/W4246287333","https://openalex.org/W4312619450","https://openalex.org/W4313588314","https://openalex.org/W4318764183","https://openalex.org/W4327638680","https://openalex.org/W4381661288","https://openalex.org/W6674118842"],"related_works":["https://openalex.org/W2846516035","https://openalex.org/W4249977926","https://openalex.org/W2585118952","https://openalex.org/W2012141574","https://openalex.org/W1606221119","https://openalex.org/W2354765335","https://openalex.org/W3123504591","https://openalex.org/W2369544116","https://openalex.org/W1691643469","https://openalex.org/W2985828462"],"abstract_inverted_index":{"In":[0],"this":[1],"publication,":[2],"we":[3],"establish":[4],"a":[5,44],"suitable":[6],"symmetry":[7],"structure":[8],"for":[9,18],"orthogonal":[10,20,23],"(\u03b1\u2212y\u2212G)-contractive":[11,21],"mappings":[12],"and":[13],"prove":[14,40],"fixed":[15,60],"point":[16,61],"results":[17,34],"an":[19,28,56],"via":[22],"metric":[24],"spaces.":[25],"We":[26],"give":[27],"application":[29],"to":[30,39,48],"strengthen":[31],"our":[32],"main":[33],"from":[35],"the":[36,41,49],"existing":[37],"literature":[38],"existence":[42],"of":[43],"unique":[45],"analytical":[46],"solution":[47],"differential":[50],"equation":[51,58],"by":[52],"converting":[53],"it":[54],"into":[55],"integral":[57],"through":[59],"analysis.":[62]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2023-09-16T00:00:00"}