{"id":"https://openalex.org/W3094678704","doi":"https://doi.org/10.1109/access.2020.3033733","title":"Anti Mandelbrot Sets via Jungck-M Iteration","display_name":"Anti Mandelbrot Sets via Jungck-M Iteration","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3094678704","doi":"https://doi.org/10.1109/access.2020.3033733","mag":"3094678704"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3033733","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3033733","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09239963.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/ielx7/6287639/8948470/09239963.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018970039","display_name":"Hengxiao Qi","orcid":"https://orcid.org/0000-0003-0911-7523"},"institutions":[{"id":"https://openalex.org/I2800350601","display_name":"Central Committee of the Communist Party of China","ror":"https://ror.org/00akhyy70","country_code":"CN","type":"government","lineage":["https://openalex.org/I2800350601"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hengxiao Qi","raw_affiliation_strings":["Party School, Shandong Provincial Committee of the Communist Party of China (Shandong Administration College), Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Party School, Shandong Provincial Committee of the Communist Party of China (Shandong Administration College), Jinan, China","institution_ids":["https://openalex.org/I2800350601"]}]},{"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"],"raw_orcid":"https://orcid.org/0000-0003-2704-353X","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/A5060234934","display_name":"Muhammad Shoaib Saleem","orcid":"https://orcid.org/0009-0002-4921-5937"},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shoaib Saleem","raw_affiliation_strings":["Department of Mathematics, University of Okara, Okara, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0050-6760","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Okara, Okara, Pakistan","institution_ids":["https://openalex.org/I3130814776"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046314241","display_name":"Yu\u2010Ming Chu","orcid":"https://orcid.org/0000-0002-0944-2134"},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuming Chu","raw_affiliation_strings":["Department of Mathematics, Huzhou University, Huzhou, China","Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-0944-2134","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huzhou University, Huzhou, China","institution_ids":["https://openalex.org/I3018263800"]},{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018970039"],"corresponding_institution_ids":["https://openalex.org/I2800350601"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":1.1743,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76606684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"8","issue":null,"first_page":"194663","last_page":"194675"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9836999773979187,"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":0.9836999773979187,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9789000153541565,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9506000280380249,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mandelbrot-set","display_name":"Mandelbrot set","score":0.9790645241737366},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.7181158661842346},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6054552793502808},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5340785980224609},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.488977313041687},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.47084495425224304},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4350664019584656},{"id":"https://openalex.org/keywords/fixed-point-iteration","display_name":"Fixed-point iteration","score":0.414287805557251},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.4116177558898926},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37869757413864136},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3637808561325073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34135007858276367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3341487944126129},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3302169740200043},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2049965262413025},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10513773560523987},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06858837604522705}],"concepts":[{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.9790645241737366},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.7181158661842346},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6054552793502808},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5340785980224609},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.488977313041687},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.47084495425224304},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4350664019584656},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.414287805557251},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.4116177558898926},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37869757413864136},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3637808561325073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34135007858276367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3341487944126129},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3302169740200043},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2049965262413025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10513773560523987},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06858837604522705},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.3033733","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3033733","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09239963.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:2a09429770ac4ba8aee42477213efd5f","is_oa":true,"landing_page_url":"https://doaj.org/article/2a09429770ac4ba8aee42477213efd5f","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":"IEEE Access, Vol 8, Pp 194663-194675 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3033733","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3033733","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09239963.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/G1064001500","display_name":null,"funder_award_id":"61673169","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G171498429","display_name":null,"funder_award_id":"11601485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4844902455","display_name":null,"funder_award_id":"11626101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4858060408","display_name":null,"funder_award_id":"11701176","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6442795590","display_name":null,"funder_award_id":"11971142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7739809515","display_name":null,"funder_award_id":"11871202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3094678704.pdf","grobid_xml":"https://content.openalex.org/works/W3094678704.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W1579586326","https://openalex.org/W1628326921","https://openalex.org/W1646303234","https://openalex.org/W1777017274","https://openalex.org/W1943365256","https://openalex.org/W1950518118","https://openalex.org/W1970847729","https://openalex.org/W1996239470","https://openalex.org/W2041966383","https://openalex.org/W2050658508","https://openalex.org/W2056966260","https://openalex.org/W2069994471","https://openalex.org/W2076234289","https://openalex.org/W2077752481","https://openalex.org/W2081637159","https://openalex.org/W2082727161","https://openalex.org/W2083642281","https://openalex.org/W2088536270","https://openalex.org/W2094347864","https://openalex.org/W2103120971","https://openalex.org/W2104332709","https://openalex.org/W2153388115","https://openalex.org/W2168865734","https://openalex.org/W2261545930","https://openalex.org/W2322987032","https://openalex.org/W2462441319","https://openalex.org/W2583994139","https://openalex.org/W2625500732","https://openalex.org/W2767011351","https://openalex.org/W2788808730","https://openalex.org/W2790540961","https://openalex.org/W2897737982","https://openalex.org/W2910668859","https://openalex.org/W2922108273","https://openalex.org/W2947234601","https://openalex.org/W2949612349","https://openalex.org/W2964631455","https://openalex.org/W2983930617","https://openalex.org/W3011424210","https://openalex.org/W3024281657","https://openalex.org/W3042793038","https://openalex.org/W3046777615","https://openalex.org/W3081318753","https://openalex.org/W3117716714","https://openalex.org/W3195342555","https://openalex.org/W4230036933","https://openalex.org/W6636666929","https://openalex.org/W6745533756","https://openalex.org/W6748383909","https://openalex.org/W6776860611","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":{"Complex":[0],"fractals":[1,20],"achieved":[2],"the":[3,7,13,19,23,29,36,42,49,61,75,80,90,98,106,112,116],"highest":[4],"popularity":[5],"in":[6,41,85,100],"last":[8],"ten":[9],"years.":[10],"Researchers":[11],"used":[12],"fixed":[14],"point":[15],"iterations":[16],"to":[17,27,114],"visualize":[18,67],"and":[21,54,66,88],"compared":[22],"image":[24,76],"generation":[25,43,77,81],"times":[26,78],"check":[28],"efficiencies":[30],"of":[31,38,44,51,82,105],"iterations.":[32],"This":[33],"article":[34],"explores":[35],"behavior":[37],"Jungck-M":[39,52],"iteration":[40,53],"anti-Mandelbrot":[45,64,83],"sets.":[46],"We":[47,59,73,95],"define":[48],"orbit":[50,87],"prove":[55],"its":[56],"escape":[57,117],"criteria.":[58],"establish":[60],"algorithm":[62],"for":[63,79],"set":[65],"some":[68],"graphs":[69,113],"via":[70],"proposed":[71,86],"iteration.":[72,94],"calculate":[74],"sets":[84],"present":[89,111],"comparison":[91],"with":[92],"Jungck-CR":[93],"also":[96],"discuss":[97],"variations":[99],"images":[101],"at":[102],"different":[103],"values":[104],"input":[107,121],"parameters.":[108,122],"Moreover,":[109],"we":[110],"show":[115],"time":[118],"depends":[119],"on":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
