{"id":"https://openalex.org/W4407253355","doi":"https://doi.org/10.3390/sym17020254","title":"Common \u03c6-Fixed Point Results for S-Operator Pair in Symmetric M-Metric Spaces","display_name":"Common \u03c6-Fixed Point Results for S-Operator Pair in Symmetric M-Metric Spaces","publication_year":2025,"publication_date":"2025-02-07","ids":{"openalex":"https://openalex.org/W4407253355","doi":"https://doi.org/10.3390/sym17020254"},"language":"en","primary_location":{"id":"doi:10.3390/sym17020254","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020254","pdf_url":"https://www.mdpi.com/2073-8994/17/2/254/pdf","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/2/254/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048298001","display_name":"Sadia Farooq","orcid":"https://orcid.org/0000-0002-5531-7561"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Sadia Farooq","raw_affiliation_strings":["Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064449182","display_name":"Naeem Saleem","orcid":"https://orcid.org/0000-0002-1485-6163"},"institutions":[{"id":"https://openalex.org/I2802393258","display_name":"Sefako Makgatho Health Sciences University","ror":"https://ror.org/003hsr719","country_code":"ZA","type":"education","lineage":["https://openalex.org/I2802393258"]},{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK","ZA"],"is_corresponding":false,"raw_author_name":"Naeem Saleem","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Medunsa, Pretoria 0204, South Africa","Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Medunsa, Pretoria 0204, South Africa","institution_ids":["https://openalex.org/I2802393258"]},{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075099807","display_name":"Maggie Aphane","orcid":"https://orcid.org/0000-0002-9640-7846"},"institutions":[{"id":"https://openalex.org/I2802393258","display_name":"Sefako Makgatho Health Sciences University","ror":"https://ror.org/003hsr719","country_code":"ZA","type":"education","lineage":["https://openalex.org/I2802393258"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Maggie Aphane","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Medunsa, Pretoria 0204, South Africa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Medunsa, Pretoria 0204, South Africa","institution_ids":["https://openalex.org/I2802393258"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011211798","display_name":"Ali Althobaiti","orcid":"https://orcid.org/0000-0001-6076-625X"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ali Althobaiti","raw_affiliation_strings":["Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048298001"],"corresponding_institution_ids":["https://openalex.org/I87482320"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04866339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"2","first_page":"254","last_page":"254"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9988999962806702,"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":0.9988999962806702,"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/T12719","display_name":"Aerospace Engineering and Energy Systems","score":0.919700026512146,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5905153751373291},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5587093234062195},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5394287109375},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5096161365509033},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.45110124349594116},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4063810706138611},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32206398248672485},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2701318562030792},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.05732220411300659},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.04881802201271057}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5905153751373291},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5587093234062195},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5394287109375},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5096161365509033},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.45110124349594116},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4063810706138611},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32206398248672485},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2701318562030792},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05732220411300659},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.04881802201271057},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17020254","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020254","pdf_url":"https://www.mdpi.com/2073-8994/17/2/254/pdf","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"}],"best_oa_location":{"id":"doi:10.3390/sym17020254","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020254","pdf_url":"https://www.mdpi.com/2073-8994/17/2/254/pdf","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/G4393481380","display_name":null,"funder_award_id":"Saudi Arabia","funder_id":"https://openalex.org/F4320323722","funder_display_name":"Taif University"},{"id":"https://openalex.org/G5679165149","display_name":null,"funder_award_id":"TU-DSPP-2024-87","funder_id":"https://openalex.org/F4320323722","funder_display_name":"Taif University"}],"funders":[{"id":"https://openalex.org/F4320323722","display_name":"Taif University","ror":"https://ror.org/014g1a453"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407253355.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1458771408","https://openalex.org/W1487976166","https://openalex.org/W1989488152","https://openalex.org/W2013281541","https://openalex.org/W2047277075","https://openalex.org/W2050391603","https://openalex.org/W2067895294","https://openalex.org/W2159491288","https://openalex.org/W2167109344","https://openalex.org/W2274736305","https://openalex.org/W2482398917","https://openalex.org/W2521763791","https://openalex.org/W2913712675","https://openalex.org/W2941900943","https://openalex.org/W2963470648","https://openalex.org/W3027959094","https://openalex.org/W3046923730","https://openalex.org/W3196836781","https://openalex.org/W4231913011","https://openalex.org/W4249666993","https://openalex.org/W4255266784","https://openalex.org/W4280595888","https://openalex.org/W4396701709","https://openalex.org/W4402189845","https://openalex.org/W4404943833","https://openalex.org/W6608219554","https://openalex.org/W6780372738","https://openalex.org/W6786918535","https://openalex.org/W6815332593"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2980963558","https://openalex.org/W172022518","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W1976691234","https://openalex.org/W3212023493","https://openalex.org/W4360593833"],"abstract_inverted_index":{"In":[0,71],"this":[1],"article,":[2],"we":[3,18],"define":[4],"a":[5,101,104,109],"new":[6],"class":[7],"of":[8,24,45,100,106],"noncommuting":[9],"self":[10],"mappings":[11],"known":[12],"as":[13],"the":[14,20,30,34,46,53,56,80,91,98,125,127],"S-operator":[15,31],"pair.":[16],"Also,":[17,123],"provide":[19],"existence":[21,99],"and":[22,42,82,114],"uniqueness":[23],"common":[25],"fixed":[26,49],"point":[27,50],"results":[28,83,92],"involving":[29],"pair":[32],"satisfying":[33],"(F,\u03c6,\u03c8,Z)-contractive":[35],"condition":[36],"in":[37,55,68,76,124],"m-metric":[38,57],"spaces,":[39],"which":[40,61],"unifies":[41],"generalizes":[43],"most":[44],"existing":[47],"relevant":[48],"theorems.":[51],"Furthermore,":[52],"variables":[54],"space":[58],"are":[59,74],"symmetric,":[60],"is":[62,132],"significant":[63],"for":[64,119],"solving":[65],"nonlinear":[66,110],"problems":[67],"operator":[69],"theory.":[70],"addition,":[72],"examples":[73],"provided":[75],"order":[77],"to":[78,96,103],"illustrate":[79],"concepts":[81],"presented":[84],"herein.":[85],"It":[86],"has":[87],"been":[88],"demonstrated":[89],"that":[90],"can":[93],"be":[94],"applied":[95],"prove":[97],"solution":[102],"system":[105],"integral":[107],"equations,":[108],"fractional":[111],"differential":[112,117],"equation":[113,118],"an":[115],"ordinary":[116],"damped":[120],"forced":[121],"oscillations.":[122],"end,":[126],"satellite":[128],"web":[129],"coupling":[130],"problem":[131],"solved.":[133]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
