{"id":"https://openalex.org/W2898967795","doi":"https://doi.org/10.3390/sym10110560","title":"Sehgal Type Contractions on b-Metric Space","display_name":"Sehgal Type Contractions on b-Metric Space","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2898967795","doi":"https://doi.org/10.3390/sym10110560","mag":"2898967795"},"language":"en","primary_location":{"id":"doi:10.3390/sym10110560","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110560","pdf_url":"https://www.mdpi.com/2073-8994/10/11/560/pdf?version=1541051489","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/2073-8994/10/11/560/pdf?version=1541051489","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113328167","display_name":"Badr Alqahtani","orcid":null},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Badr Alqahtani","raw_affiliation_strings":["Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031136190","display_name":"Andreea Fulga","orcid":"https://orcid.org/0000-0002-6689-0355"},"institutions":[{"id":"https://openalex.org/I3123573182","display_name":"Transylvania University of Bra\u0219ov","ror":"https://ror.org/01cg9ws23","country_code":"RO","type":"education","lineage":["https://openalex.org/I3123573182"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Andreea Fulga","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, Brasov 500036, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, Brasov 500036, Romania","institution_ids":["https://openalex.org/I3123573182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081792390","display_name":"Erdal Karap\u0131nar","orcid":"https://orcid.org/0000-0002-6798-3254"},"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/I45542416","display_name":"Atilim University","ror":"https://ror.org/04pd3v454","country_code":"TR","type":"education","lineage":["https://openalex.org/I45542416"]}],"countries":["TR","TW"],"is_corresponding":true,"raw_author_name":"Erdal Karap\u0131nar","raw_affiliation_strings":["Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey","Department of Medical Research, China Medical University, Taichung 40402, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-6798-3254","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey","institution_ids":["https://openalex.org/I45542416"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081792390"],"corresponding_institution_ids":["https://openalex.org/I184693016","https://openalex.org/I45542416"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.5242,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82341456,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"10","issue":"11","first_page":"560","last_page":"560"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.979200005531311,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/uniqueness","display_name":"Uniqueness","score":0.7653711438179016},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6698507070541382},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6640858054161072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6434402465820312},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.6206772923469543},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5601696968078613},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.541163980960846},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4909665882587433},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4480399191379547},{"id":"https://openalex.org/keywords/aggregate","display_name":"Aggregate (composite)","score":0.42306041717529297},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39505988359451294},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3714890480041504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2864067852497101},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04907631874084473}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7653711438179016},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6698507070541382},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6640858054161072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6434402465820312},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6206772923469543},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5601696968078613},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.541163980960846},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4909665882587433},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4480399191379547},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.42306041717529297},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39505988359451294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3714890480041504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2864067852497101},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04907631874084473},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym10110560","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110560","pdf_url":"https://www.mdpi.com/2073-8994/10/11/560/pdf?version=1541051489","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:2a4f0ba72a8e4d0f97196934f06e0632","is_oa":true,"landing_page_url":"https://doaj.org/article/2a4f0ba72a8e4d0f97196934f06e0632","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":"Symmetry, Vol 10, Iss 11, p 560 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/11/560/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10110560","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym10110560","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110560","pdf_url":"https://www.mdpi.com/2073-8994/10/11/560/pdf?version=1541051489","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":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2898967795.pdf","grobid_xml":"https://content.openalex.org/works/W2898967795.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W72134831","https://openalex.org/W1487404658","https://openalex.org/W1973461813","https://openalex.org/W1985195480","https://openalex.org/W1988476861","https://openalex.org/W2007924402","https://openalex.org/W2015222848","https://openalex.org/W2036759414","https://openalex.org/W2060627367","https://openalex.org/W2283642325","https://openalex.org/W2472218344","https://openalex.org/W2473587624","https://openalex.org/W2562964995","https://openalex.org/W2782694957","https://openalex.org/W2895461855","https://openalex.org/W6602953246","https://openalex.org/W6659585781","https://openalex.org/W6720658594"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4390756076","https://openalex.org/W4243074410"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,37,56],"analyze":[4],"two":[5],"discontinuous":[6],"self-mappings":[7],"that":[8],"satisfy":[9],"Sehgal-type":[10],"inequalities":[11],"in":[12,32],"the":[13,23,33,44,58,63,68],"setup":[14],"of":[15,22,48,67],"complete":[16],"b-metric":[17],"space.":[18],"The":[19],"main":[20],"results":[21,31],"paper":[24],"cover":[25],"and":[26,46,65],"extend":[27],"a":[28],"few":[29],"existing":[30],"corresponding":[34],"literature.":[35],"Furthermore,":[36],"give":[38],"some":[39],"illustrative":[40],"examples":[41],"to":[42,61],"verify":[43],"effectiveness":[45],"strength":[47],"our":[49],"derived":[50],"results.":[51],"Thereafter,":[52],"as":[53],"an":[54],"application,":[55],"consider":[57],"obtained":[59],"result":[60],"aggregate":[62],"existence":[64],"uniqueness":[66],"solution":[69],"for":[70],"nonlinear":[71],"Fredholm":[72],"integral":[73],"equations.":[74]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
