{"id":"https://openalex.org/W2983930617","doi":"https://doi.org/10.1109/access.2019.2951385","title":"Fixed Point Results for Fractal Generation in Extended Jungck\u2013SP Orbit","display_name":"Fixed Point Results for Fractal Generation in Extended Jungck\u2013SP Orbit","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2983930617","doi":"https://doi.org/10.1109/access.2019.2951385","mag":"2983930617"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2951385","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2951385","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08890803.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08890803.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100341802","display_name":"Xiang\u2010Yang Li","orcid":"https://orcid.org/0000-0002-6070-6625"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiangyang Li","raw_affiliation_strings":["College of Digital Technology and Engineering, Ningbo University of Finance and Economics, Ningbo, China"],"affiliations":[{"raw_affiliation_string":"College of Digital Technology and Engineering, Ningbo University of Finance and Economics, Ningbo, China","institution_ids":["https://openalex.org/I109935558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100731084","display_name":"Muhammad Tanveer","orcid":"https://orcid.org/0000-0003-2704-353X"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Tanveer","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I142204992"]}]},{"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/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]},{"id":"https://openalex.org/I69552723","display_name":"University of Pretoria","ror":"https://ror.org/00g0p6g84","country_code":"ZA","type":"education","lineage":["https://openalex.org/I69552723"]}],"countries":["PK","ZA"],"is_corresponding":false,"raw_author_name":"Mujahid Abbas","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore, Pakistan","Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa","institution_ids":["https://openalex.org/I69552723"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043740401","display_name":"Maqbool Ahmad","orcid":"https://orcid.org/0000-0001-8621-4541"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Maqbool Ahmad","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I142204992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005443260","display_name":"Young Chel Kwun","orcid":"https://orcid.org/0000-0002-5028-0640"},"institutions":[{"id":"https://openalex.org/I51226738","display_name":"Dong-A University","ror":"https://ror.org/03qvtpc38","country_code":"KR","type":"education","lineage":["https://openalex.org/I51226738"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Young Chel Kwun","raw_affiliation_strings":["Department of Mathematics, Dong-A University, Busan, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dong-A University, Busan, South Korea","institution_ids":["https://openalex.org/I51226738"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025149741","display_name":"Jing Liu","orcid":"https://orcid.org/0000-0001-5035-2053"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Liu","raw_affiliation_strings":["College of Digital Technology and Engineering, Ningbo University of Finance and Economics, Ningbo, China"],"affiliations":[{"raw_affiliation_string":"College of Digital Technology and Engineering, Ningbo University of Finance and Economics, Ningbo, China","institution_ids":["https://openalex.org/I109935558"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5100341802"],"corresponding_institution_ids":["https://openalex.org/I109935558"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.0535,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.92034426,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"7","issue":null,"first_page":"160472","last_page":"160481"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9997000098228455,"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":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9842000007629395,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9779000282287598,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.7389272451400757},{"id":"https://openalex.org/keywords/mandelbrot-set","display_name":"Mandelbrot set","score":0.652350664138794},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6403604745864868},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.634154200553894},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.6017409563064575},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.49594172835350037},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45610669255256653},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.45491647720336914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4345041811466217},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4194951355457306},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40203237533569336},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16876083612442017},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12883907556533813},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09941783547401428},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07821276783943176}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.7389272451400757},{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.652350664138794},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6403604745864868},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.634154200553894},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.6017409563064575},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.49594172835350037},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45610669255256653},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.45491647720336914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4345041811466217},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4194951355457306},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40203237533569336},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16876083612442017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12883907556533813},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09941783547401428},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07821276783943176},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/access.2019.2951385","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2951385","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08890803.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f64283fc7f21471fb33e9bd23031a917","is_oa":true,"landing_page_url":"https://doaj.org/article/f64283fc7f21471fb33e9bd23031a917","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 160472-160481 (2019)","raw_type":"article"},{"id":"pmh:oai:repository.up.ac.za:2263/74648","is_oa":true,"landing_page_url":"http://hdl.handle.net/2263/74648","pdf_url":null,"source":{"id":"https://openalex.org/S4306401870","display_name":"UpSpace Institutional Repository (University of Pretoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I69552723","host_organization_name":"University of Pretoria","host_organization_lineage":["https://openalex.org/I69552723"],"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":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2951385","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2951385","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08890803.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G955972602","display_name":null,"funder_award_id":"2017A610105","funder_id":"https://openalex.org/F4320332587","funder_display_name":"Natural Science Foundation of Ningbo"}],"funders":[{"id":"https://openalex.org/F4320332587","display_name":"Natural Science Foundation of Ningbo","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2983930617.pdf","grobid_xml":"https://content.openalex.org/works/W2983930617.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1628326921","https://openalex.org/W1777017274","https://openalex.org/W1943365256","https://openalex.org/W1950518118","https://openalex.org/W1968965098","https://openalex.org/W2040306943","https://openalex.org/W2041966383","https://openalex.org/W2050658508","https://openalex.org/W2056038242","https://openalex.org/W2059419450","https://openalex.org/W2076234289","https://openalex.org/W2082727161","https://openalex.org/W2083642281","https://openalex.org/W2094347864","https://openalex.org/W2104332709","https://openalex.org/W2153388115","https://openalex.org/W2182230374","https://openalex.org/W2186949102","https://openalex.org/W2247509386","https://openalex.org/W2261545930","https://openalex.org/W2319365926","https://openalex.org/W2322987032","https://openalex.org/W2352978371","https://openalex.org/W2583994139","https://openalex.org/W2587732019","https://openalex.org/W2625500732","https://openalex.org/W2757730116","https://openalex.org/W2767011351","https://openalex.org/W2790540961","https://openalex.org/W2803712475","https://openalex.org/W2807565888","https://openalex.org/W2897737982","https://openalex.org/W2910668859","https://openalex.org/W2922108273","https://openalex.org/W2947234601","https://openalex.org/W2964631455","https://openalex.org/W3195342555","https://openalex.org/W6685483940","https://openalex.org/W6705513857","https://openalex.org/W6711739752","https://openalex.org/W6745533756","https://openalex.org/W6800049010"],"related_works":["https://openalex.org/W3041627746","https://openalex.org/W2156263007","https://openalex.org/W36806243","https://openalex.org/W2385956173","https://openalex.org/W626480733","https://openalex.org/W2389069788","https://openalex.org/W621136261","https://openalex.org/W1557532642","https://openalex.org/W4237800857","https://openalex.org/W4388292962"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,45],"extend":[4],"Jungck\u2013SP":[5,56],"iteration":[6,33],"with":[7,58,77],"<inline-formula":[8,59],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,60],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[10,61],"<tex-math":[11,62],"notation=\"LaTeX\">$s$":[12,63],"</tex-math></inline-formula>":[13,64],"\u2013convexity":[14],"in":[15,55,75],"second":[16],"sense":[17],"and":[18,34,52],"define":[19],"its":[20],"orbit.":[21],"We":[22,66],"prove":[23],"the":[24,73],"fixed":[25],"point":[26],"results":[27,37],"for":[28,41],"fractal":[29,42],"generation":[30],"via":[31],"extended":[32],"utilize":[35],"these":[36],"to":[38,71],"develop":[39],"algorithms":[40],"visualization.":[43],"Moreover,":[44],"present":[46,68],"some":[47,69],"complex":[48],"graphs":[49],"of":[50],"Julia":[51],"Mandelbrot":[53],"sets":[54],"orbit":[57],"\u2013convexity.":[65],"also":[67],"examples":[70],"show":[72],"variation":[74],"images":[76],"involved":[78],"parameters.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2019-11-22T00:00:00"}
