{"id":"https://openalex.org/W4323663584","doi":"https://doi.org/10.3390/sym15030686","title":"Fixed Point Approaches for Multi-Valued Pre\u0161i\u0107 Multi-Step Iterative Mappings with Applications","display_name":"Fixed Point Approaches for Multi-Valued Pre\u0161i\u0107 Multi-Step Iterative Mappings with Applications","publication_year":2023,"publication_date":"2023-03-09","ids":{"openalex":"https://openalex.org/W4323663584","doi":"https://doi.org/10.3390/sym15030686"},"language":"en","primary_location":{"id":"doi:10.3390/sym15030686","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030686","pdf_url":"https://www.mdpi.com/2073-8994/15/3/686/pdf?version=1678329372","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/2073-8994/15/3/686/pdf?version=1678329372","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062188430","display_name":"Ali Raza","orcid":"https://orcid.org/0000-0002-0616-8520"},"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":false,"raw_author_name":"Ali Raza","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0616-8520","affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054055136","display_name":"Mujahid Abbas","orcid":"https://orcid.org/0000-0001-5528-1207"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"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","TW"],"is_corresponding":false,"raw_author_name":"Mujahid Abbas","raw_affiliation_strings":["Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan","Department of Medical Research, China Medical University, Taichung 404, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I43879129"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University, Taichung 404, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045162488","display_name":"Hasanen A. Hammad","orcid":"https://orcid.org/0000-0001-8724-9367"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]},{"id":"https://openalex.org/I97455420","display_name":"Sohag University","ror":"https://ror.org/02wgx3e98","country_code":"EG","type":"education","lineage":["https://openalex.org/I97455420"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"Hasanen A. Hammad","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt","Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-8724-9367","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt","institution_ids":["https://openalex.org/I97455420"]},{"raw_affiliation_string":"Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042326806","display_name":"Manuel De la Sen","orcid":"https://orcid.org/0000-0001-9320-9433"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Manuel De la Sen","raw_affiliation_strings":["Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9320-9433","affiliations":[{"raw_affiliation_string":"Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Spain","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5045162488"],"corresponding_institution_ids":["https://openalex.org/I156216236","https://openalex.org/I97455420"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5315,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56782495,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"3","first_page":"686","last_page":"686"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9501000046730042,"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/fixed-point","display_name":"Fixed point","score":0.6584824323654175},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.530586838722229},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5020191669464111},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.49360191822052},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4862560033798218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48369914293289185},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.48164263367652893},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.47150248289108276},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.46890580654144287},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45734477043151855},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4437254071235657},{"id":"https://openalex.org/keywords/iterative-and-incremental-development","display_name":"Iterative and incremental development","score":0.42398643493652344},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4126644432544708},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3571428656578064},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32636767625808716},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2584773004055023},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08074867725372314}],"concepts":[{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6584824323654175},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.530586838722229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5020191669464111},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.49360191822052},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4862560033798218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48369914293289185},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48164263367652893},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.47150248289108276},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.46890580654144287},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45734477043151855},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4437254071235657},{"id":"https://openalex.org/C143587482","wikidata":"https://www.wikidata.org/wiki/Q1543216","display_name":"Iterative and incremental development","level":2,"score":0.42398643493652344},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4126644432544708},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3571428656578064},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32636767625808716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2584773004055023},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08074867725372314},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym15030686","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030686","pdf_url":"https://www.mdpi.com/2073-8994/15/3/686/pdf?version=1678329372","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:addi.ehu.eus:10810/60556","is_oa":true,"landing_page_url":"http://hdl.handle.net/10810/60556","pdf_url":"http://addi.ehu.es/bitstream/10810/60556/1/symmetry-15-00686.pdf","source":{"id":"https://openalex.org/S4306401964","display_name":"Communities in ADDI (University of the Basque Country)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169108374","host_organization_name":"University of the Basque Country","host_organization_lineage":["https://openalex.org/I169108374"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:eb78b2cb47184bca8d96b46b35de2414","is_oa":false,"landing_page_url":"https://doaj.org/article/eb78b2cb47184bca8d96b46b35de2414","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 3, p 686 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/3/686/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15030686","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":"Symmetry; Volume 15; Issue 3; Pages: 686","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15030686","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030686","pdf_url":"https://www.mdpi.com/2073-8994/15/3/686/pdf?version=1678329372","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/G3497146170","display_name":null,"funder_award_id":"IT1555-22","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"}],"funders":[{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4323663584.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W34096310","https://openalex.org/W1458771408","https://openalex.org/W1872584069","https://openalex.org/W1967815257","https://openalex.org/W1977620557","https://openalex.org/W1981459842","https://openalex.org/W1982397835","https://openalex.org/W2002459675","https://openalex.org/W2014713709","https://openalex.org/W2060639087","https://openalex.org/W2072623541","https://openalex.org/W2078672636","https://openalex.org/W2094611044","https://openalex.org/W2112243044","https://openalex.org/W2115467840","https://openalex.org/W2122440577","https://openalex.org/W2123009642","https://openalex.org/W2129941846","https://openalex.org/W2165967902","https://openalex.org/W2491467784","https://openalex.org/W2555809946","https://openalex.org/W2735798520","https://openalex.org/W2783306445","https://openalex.org/W2908470519","https://openalex.org/W2954773144","https://openalex.org/W3032246484","https://openalex.org/W3035689151","https://openalex.org/W3112608024","https://openalex.org/W3131182242","https://openalex.org/W3152009687","https://openalex.org/W3154169191","https://openalex.org/W3169756336","https://openalex.org/W3183630953","https://openalex.org/W4206357596","https://openalex.org/W4210663079","https://openalex.org/W4280609545","https://openalex.org/W4385284220","https://openalex.org/W6674118842","https://openalex.org/W7024499617"],"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":{"The":[0],"purpose":[1],"of":[2,53,61],"this":[3],"paper":[4],"is":[5,71],"to":[6,27,42,64],"present":[7],"some":[8,23,51],"fixed":[9],"point":[10],"approaches":[11],"for":[12],"multi-valued":[13],"Pre\u0161i\u0107":[14],"k-step":[15],"iterative-type":[16],"mappings":[17],"on":[18],"a":[19,62],"metric":[20],"space.":[21],"Furthermore,":[22],"corollaries":[24],"are":[25,40,56],"obtained":[26],"unify":[28],"and":[29,58],"extend":[30],"many":[31],"symmetrical":[32],"results":[33],"in":[34],"the":[35,44,59,65],"literature.":[36],"Moreover,":[37],"two":[38],"examples":[39],"provided":[41],"support":[43],"main":[45],"result.":[46],"Ultimately,":[47],"as":[48],"potential":[49],"applications,":[50],"contributions":[52],"integral":[54],"type":[55],"investigated":[57],"existence":[60],"solution":[63],"second-order":[66],"boundary":[67],"value":[68],"problem":[69],"(BVP)":[70],"presented.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}