{"id":"https://openalex.org/W4396592213","doi":"https://doi.org/10.3390/sym16050546","title":"Strong and Weak Convergence Theorems for the Split Feasibility Problem of (\u03b2,k)-Enriched Strict Pseudocontractive Mappings with an Application in Hilbert Spaces","display_name":"Strong and Weak Convergence Theorems for the Split Feasibility Problem of (\u03b2,k)-Enriched Strict Pseudocontractive Mappings with an Application in Hilbert Spaces","publication_year":2024,"publication_date":"2024-05-02","ids":{"openalex":"https://openalex.org/W4396592213","doi":"https://doi.org/10.3390/sym16050546"},"language":"en","primary_location":{"id":"doi:10.3390/sym16050546","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16050546","pdf_url":"https://www.mdpi.com/2073-8994/16/5/546/pdf?version=1714637475","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/2073-8994/16/5/546/pdf?version=1714637475","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055955473","display_name":"Asima Razzaque","orcid":"https://orcid.org/0000-0002-7579-8972"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Asima Razzaque","raw_affiliation_strings":["Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia","Department of Mathematics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-7579-8972","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"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":true,"raw_author_name":"Naeem Saleem","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa","Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1485-6163","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, 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/A5070146005","display_name":"Imo Kalu Agwu","orcid":null},"institutions":[{"id":"https://openalex.org/I98220444","display_name":"Michael Okpara University of Agriculture","ror":"https://ror.org/050850526","country_code":"NG","type":"education","lineage":["https://openalex.org/I98220444"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Imo Kalu Agwu","raw_affiliation_strings":["Department of Mathematics, Michael Okpara University of Agriculture, Umudike 440101, Abia State, Nigeria"],"raw_orcid":"https://orcid.org/0000-0003-4535-1974","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michael Okpara University of Agriculture, Umudike 440101, Abia State, Nigeria","institution_ids":["https://openalex.org/I98220444"]}]},{"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":"https://orcid.org/0000-0002-5228-1073","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"last","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, Pretoria 0204, South Africa"],"raw_orcid":"https://orcid.org/0000-0002-9640-7846","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa","institution_ids":["https://openalex.org/I2802393258"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5055955473","https://openalex.org/A5064449182"],"corresponding_institution_ids":["https://openalex.org/I2802393258","https://openalex.org/I4626487","https://openalex.org/I87482320"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06922001,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"5","first_page":"546","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9800999760627747,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9599000215530396,"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/hilbert-space","display_name":"Hilbert space","score":0.8980969786643982},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7218745946884155},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.711411714553833},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.650036096572876},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5819973945617676},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.48206883668899536},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4280860722064972},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.42432066798210144},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4109220504760742},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3799520432949066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24907070398330688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23336219787597656}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.8980969786643982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7218745946884155},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.711411714553833},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.650036096572876},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5819973945617676},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48206883668899536},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4280860722064972},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.42432066798210144},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4109220504760742},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3799520432949066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24907070398330688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23336219787597656},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16050546","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16050546","pdf_url":"https://www.mdpi.com/2073-8994/16/5/546/pdf?version=1714637475","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:0f15a3c6416f439c925b84376fba1baf","is_oa":false,"landing_page_url":"https://doaj.org/article/0f15a3c6416f439c925b84376fba1baf","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 16, Iss 5, p 546 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16050546","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16050546","pdf_url":"https://www.mdpi.com/2073-8994/16/5/546/pdf?version=1714637475","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4396592213.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1685874591","https://openalex.org/W1938673097","https://openalex.org/W1980980706","https://openalex.org/W2001504573","https://openalex.org/W2042314419","https://openalex.org/W2052565283","https://openalex.org/W2067653858","https://openalex.org/W2095201608","https://openalex.org/W2108917141","https://openalex.org/W2150158377","https://openalex.org/W2155038429","https://openalex.org/W2158227330","https://openalex.org/W2220044512","https://openalex.org/W2298899400","https://openalex.org/W3013846195","https://openalex.org/W3196902267","https://openalex.org/W3212153577","https://openalex.org/W4280595888","https://openalex.org/W4281629029","https://openalex.org/W4285729039","https://openalex.org/W4294635773","https://openalex.org/W4403403933","https://openalex.org/W6640712999","https://openalex.org/W6680415720","https://openalex.org/W6803756491"],"related_works":["https://openalex.org/W2053463107","https://openalex.org/W1991765628","https://openalex.org/W2055132062","https://openalex.org/W2330072811","https://openalex.org/W1987269275","https://openalex.org/W2381443067","https://openalex.org/W2121115887","https://openalex.org/W2058725647","https://openalex.org/W3143755272","https://openalex.org/W2011881806"],"abstract_inverted_index":{"The":[0],"concept":[1],"of":[2,17,52,55,63,70,96,116,140],"symmetry":[3],"has":[4],"played":[5],"a":[6,18,50,64,137,154],"major":[7],"role":[8],"in":[9,60,120,129,147,153,168],"Hilbert":[10,35,66,156],"space":[11],"setting":[12],"owing":[13],"to":[14,27,44],"the":[15,42,61,84,94,112,117,169],"structure":[16],"complete":[19],"inner":[20],"product":[21],"space.":[22,67,157],"Subsequently,":[23],"different":[24],"studies":[25],"pertaining":[26],"symmetry,":[28],"including":[29],"symmetric":[30],"operators,":[31],"have":[32],"investigated":[33],"real":[34,65,155],"spaces.":[36],"In":[37,68,132],"this":[38,87,130],"paper,":[39],"we":[40,72,134],"study":[41],"solutions":[43,97],"multiple-set":[45],"split":[46],"feasibility":[47],"problems":[48,152],"for":[49,93,125],"pair":[51],"finite":[53,114],"families":[54],"\u03b2-enriched,":[56],"strictly":[57],"pseudocontractive":[58],"mappings":[59,82],"setup":[62],"view":[69],"this,":[71],"constructed":[73],"an":[74,90],"iterative":[75,88,142],"scheme":[76,143],"that":[77,136],"properly":[78],"included":[79],"these":[80],"two":[81],"into":[83],"formula.":[85],"Under":[86],"scheme,":[89],"appropriate":[91],"condition":[92,108],"existence":[95],"and":[98,100,162],"strong":[99],"weak":[101],"convergent":[102],"results":[103,123,128,159,165],"are":[104],"presented.":[105],"No":[106],"sum":[107],"is":[109],"imposed":[110],"on":[111],"countably":[113],"family":[115],"iteration":[118],"parameters":[119],"obtaining":[121],"our":[122,141],"unlike":[124],"several":[126,164],"other":[127],"direction.":[131],"addition,":[133],"prove":[135],"slight":[138],"modification":[139],"could":[144],"be":[145],"applied":[146],"studying":[148],"hierarchical":[149],"variational":[150],"inequality":[151],"Our":[158],"improve,":[160],"extend":[161],"generalize":[163],"currently":[166],"existing":[167],"literature.":[170]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
