{"id":"https://openalex.org/W4401697107","doi":"https://doi.org/10.3390/axioms13080562","title":"Enriched Z-Contractions and Fixed-Point Results with Applications to IFS","display_name":"Enriched Z-Contractions and Fixed-Point Results with Applications to IFS","publication_year":2024,"publication_date":"2024-08-19","ids":{"openalex":"https://openalex.org/W4401697107","doi":"https://doi.org/10.3390/axioms13080562"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13080562","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080562","pdf_url":"https://www.mdpi.com/2075-1680/13/8/562/pdf?version=1724070755","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/2075-1680/13/8/562/pdf?version=1724070755","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037842585","display_name":"Ibrahim Alraddadi","orcid":"https://orcid.org/0000-0002-0094-7937"},"institutions":[{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ibrahim Alraddadi","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-0094-7937","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia","institution_ids":["https://openalex.org/I4210151290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030383092","display_name":"Muhammad Din","orcid":"https://orcid.org/0009-0009-2396-2943"},"institutions":[{"id":"https://openalex.org/I108108428","display_name":"Thammasat University","ror":"https://ror.org/002yp7f20","country_code":"TH","type":"education","lineage":["https://openalex.org/I108108428"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Muhammad Din","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, Thailand"],"raw_orcid":"https://orcid.org/0009-0009-2396-2943","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, Thailand","institution_ids":["https://openalex.org/I108108428"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045304341","display_name":"Umar Ishtiaq","orcid":"https://orcid.org/0000-0002-5228-1073"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Umar Ishtiaq","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035823439","display_name":"Mohammad Akram","orcid":"https://orcid.org/0000-0003-1416-5351"},"institutions":[{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Mohammad Akram","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia","institution_ids":["https://openalex.org/I4210151290"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087674067","display_name":"Ioannis K. Argyros","orcid":"https://orcid.org/0000-0002-9189-9298"},"institutions":[{"id":"https://openalex.org/I113618177","display_name":"Cameron University","ror":"https://ror.org/00rgv0036","country_code":"US","type":"education","lineage":["https://openalex.org/I113618177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ioannis K. Argyros","raw_affiliation_strings":["Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5035823439","https://openalex.org/A5087674067"],"corresponding_institution_ids":["https://openalex.org/I113618177","https://openalex.org/I4210151290"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.4315,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.87898146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"13","issue":"8","first_page":"562","last_page":"562"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9968000054359436,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9968000054359436,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9824000000953674,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9782000184059143,"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/fixed-point","display_name":"Fixed point","score":0.45451945066452026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3790290653705597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34983399510383606},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15085631608963013}],"concepts":[{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.45451945066452026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3790290653705597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34983399510383606},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15085631608963013}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms13080562","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080562","pdf_url":"https://www.mdpi.com/2075-1680/13/8/562/pdf?version=1724070755","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:7eb0b932a39943f39546226c6fcd4a10","is_oa":true,"landing_page_url":"https://doaj.org/article/7eb0b932a39943f39546226c6fcd4a10","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 8, p 562 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/13/8/562/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms13080562","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms13080562","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080562","pdf_url":"https://www.mdpi.com/2075-1680/13/8/562/pdf?version=1724070755","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":[],"funders":[{"id":"https://openalex.org/F4320331150","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401697107.pdf","grobid_xml":"https://content.openalex.org/works/W4401697107.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1458771408","https://openalex.org/W1515581421","https://openalex.org/W1558948865","https://openalex.org/W1977525095","https://openalex.org/W1977620557","https://openalex.org/W2006137460","https://openalex.org/W2006600811","https://openalex.org/W2017482687","https://openalex.org/W2029537334","https://openalex.org/W2057814105","https://openalex.org/W2781214971","https://openalex.org/W3013846195","https://openalex.org/W4249775755","https://openalex.org/W4285214213","https://openalex.org/W4308208237","https://openalex.org/W4313511858","https://openalex.org/W4361283629","https://openalex.org/W4385973445","https://openalex.org/W4386829594","https://openalex.org/W4386886831","https://openalex.org/W4387020840","https://openalex.org/W4391875632","https://openalex.org/W6644762099"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1],"manuscript,":[2],"we":[3,76],"initiate":[4],"a":[5],"large":[6],"class":[7],"of":[8,21,25,45,100,107,135],"enriched":[9,84,92,111],"(d,Z)-Z-contractions":[10,85,112],"defined":[11],"on":[12],"Banach":[13,87],"spaces":[14,88],"and":[15,19,37,60,89,104,126],"prove":[16],"the":[17,22,43,46,49,56,62,78,91,98,105,108,132],"existence":[18,40,63],"uniqueness":[20,44,106],"fixed":[23],"point":[24],"these":[26],"contractions.":[27],"We":[28],"also":[29,114,122],"provide":[30],"an":[31,39],"example":[32],"to":[33,48],"support":[34],"our":[35],"results":[36,53,70],"give":[38],"condition":[41],"for":[42],"solution":[47],"integral":[50],"equation.":[51],"The":[52],"provided":[54],"in":[55,86,131],"manuscript":[57],"extend,":[58],"generalize,":[59],"modify":[61],"results.":[64],"Our":[65,116],"research":[66],"introduces":[67],"novel":[68],"fixed-point":[69],"under":[71],"various":[72],"contractive":[73],"conditions.":[74],"Furthermore,":[75],"discuss":[77],"iterated":[79],"function":[80],"system":[81],"associated":[82],"with":[83],"define":[90],"Z-Hutchinson":[93],"operator.":[94],"A":[95],"result":[96],"regarding":[97],"convergence":[99],"Krasnoselskii\u2019s":[101],"iteration":[102],"method":[103],"attractor":[109],"via":[110],"is":[113],"established.":[115],"discoveries":[117],"not":[118],"only":[119],"confirm":[120],"but":[121],"significantly":[123],"build":[124],"upon":[125],"broaden":[127],"several":[128],"established":[129],"findings":[130],"current":[133],"body":[134],"literature.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-06-09T15:46:55.921056","created_date":"2024-08-20T00:00:00"}