{"id":"https://openalex.org/W3084066188","doi":"https://doi.org/10.3390/sym12111825","title":"Fixed Circle and Fixed Disc Results for New Types of \u0398c-Contractive Mappings in Metric Spaces","display_name":"Fixed Circle and Fixed Disc Results for New Types of \u0398c-Contractive Mappings in Metric Spaces","publication_year":2020,"publication_date":"2020-11-04","ids":{"openalex":"https://openalex.org/W3084066188","doi":"https://doi.org/10.3390/sym12111825","mag":"3084066188"},"language":"en","primary_location":{"id":"doi:10.3390/sym12111825","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12111825","pdf_url":"https://www.mdpi.com/2073-8994/12/11/1825/pdf?version=1604463636","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/2073-8994/12/11/1825/pdf?version=1604463636","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027789440","display_name":"Hayel N. Saleh","orcid":"https://orcid.org/0000-0002-8343-4036"},"institutions":[{"id":"https://openalex.org/I171210897","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02","country_code":"IN","type":"education","lineage":["https://openalex.org/I171210897"]},{"id":"https://openalex.org/I36197038","display_name":"Taiz University","ror":"https://ror.org/03jwcxq96","country_code":"YE","type":"education","lineage":["https://openalex.org/I36197038"]}],"countries":["IN","YE"],"is_corresponding":false,"raw_author_name":"Hayel N. Saleh","raw_affiliation_strings":["Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India","Department of Mathematics, Taiz University, Taiz 6803, Yemen"],"raw_orcid":"https://orcid.org/0000-0002-8343-4036","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India","institution_ids":["https://openalex.org/I171210897"]},{"raw_affiliation_string":"Department of Mathematics, Taiz University, Taiz 6803, Yemen","institution_ids":["https://openalex.org/I36197038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032241746","display_name":"Salvatore Sessa","orcid":"https://orcid.org/0000-0002-4303-2884"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Salvatore Sessa","raw_affiliation_strings":["Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"],"raw_orcid":"https://orcid.org/0000-0002-4303-2884","affiliations":[{"raw_affiliation_string":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044216986","display_name":"Waleed M. Alfaqih","orcid":"https://orcid.org/0000-0001-6281-1229"},"institutions":[{"id":"https://openalex.org/I29891158","display_name":"University of Sharjah","ror":"https://ror.org/00engpz63","country_code":"AE","type":"education","lineage":["https://openalex.org/I29891158"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Waleed M. Alfaqih","raw_affiliation_strings":["Department of Mathematics, Hajjah University, Hajjah 1729, Yemen"],"raw_orcid":"https://orcid.org/0000-0001-6281-1229","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hajjah University, Hajjah 1729, Yemen","institution_ids":["https://openalex.org/I29891158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090086784","display_name":"Mohammad Imdad","orcid":"https://orcid.org/0000-0003-3270-1365"},"institutions":[{"id":"https://openalex.org/I171210897","display_name":"Aligarh Muslim University","ror":"https://ror.org/03kw9gc02","country_code":"IN","type":"education","lineage":["https://openalex.org/I171210897"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mohammad Imdad","raw_affiliation_strings":["Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"],"raw_orcid":"https://orcid.org/0000-0003-3270-1365","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India","institution_ids":["https://openalex.org/I171210897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021626938","display_name":"Nabil Mlaiki","orcid":"https://orcid.org/0000-0002-7986-886X"},"institutions":[{"id":"https://openalex.org/I142024983","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26","country_code":"SA","type":"education","lineage":["https://openalex.org/I142024983"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Nabil Mlaiki","raw_affiliation_strings":["Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-7986-886X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032241746"],"corresponding_institution_ids":["https://openalex.org/I71267560"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.0966,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91678712,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"12","issue":"11","first_page":"1825","last_page":"1825"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.8473995923995972},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7170494198799133},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6085629463195801},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47016116976737976},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.46914902329444885},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.44730326533317566},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.4300042986869812},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3675200939178467},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.199629008769989}],"concepts":[{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.8473995923995972},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7170494198799133},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6085629463195801},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47016116976737976},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.46914902329444885},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.44730326533317566},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.4300042986869812},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3675200939178467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.199629008769989},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12111825","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12111825","pdf_url":"https://www.mdpi.com/2073-8994/12/11/1825/pdf?version=1604463636","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:19f41ce21c7c48eb85894850fe40be3f","is_oa":true,"landing_page_url":"https://doaj.org/article/19f41ce21c7c48eb85894850fe40be3f","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 12, Iss 11, p 1825 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/11/1825/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12111825","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/sym12111825","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12111825","pdf_url":"https://www.mdpi.com/2073-8994/12/11/1825/pdf?version=1604463636","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3084066188.pdf","grobid_xml":"https://content.openalex.org/works/W3084066188.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1458771408","https://openalex.org/W1868485006","https://openalex.org/W2000829143","https://openalex.org/W2012066174","https://openalex.org/W2048884582","https://openalex.org/W2094611044","https://openalex.org/W2107929732","https://openalex.org/W2116341502","https://openalex.org/W2116659777","https://openalex.org/W2138309213","https://openalex.org/W2332549331","https://openalex.org/W2591713368","https://openalex.org/W2777559831","https://openalex.org/W2784261406","https://openalex.org/W2795368455","https://openalex.org/W2895768238","https://openalex.org/W2900322214","https://openalex.org/W2900361771","https://openalex.org/W2910485676","https://openalex.org/W2913712675","https://openalex.org/W2915254468","https://openalex.org/W2981423257","https://openalex.org/W2989822137","https://openalex.org/W3098132778","https://openalex.org/W3160782560","https://openalex.org/W6747308087","https://openalex.org/W6795215480"],"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":{"In":[0],"this":[1],"manuscript,":[2],"we":[3,14,40],"introduce":[4],"the":[5,24,63],"notions":[6],"of":[7,10,26,49,58],"various":[8],"types":[9],"\u0398c-contractions":[11],"for":[12],"which":[13,54],"establish":[15],"some":[16,42],"fixed":[17,20,43,46],"circle":[18,44],"and":[19,45,60],"disc":[21,47],"theorems":[22],"in":[23,62],"setting":[25],"metric":[27],"spaces.":[28],"Some":[29],"illustrative":[30],"examples":[31],"are":[32],"also":[33],"provided":[34],"to":[35],"support":[36],"our":[37],"results.":[38],"Moreover,":[39],"present":[41],"results":[48,57],"integral":[50],"type":[51],"contractive":[52],"self-mappings,":[53],"generalize":[55],"many":[56],"invariance":[59],"transformations":[61],"literature.":[64]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}