{"id":"https://openalex.org/W2149820609","doi":"https://doi.org/10.1155/2012/526503","title":"On the Rate of Convergence of Kirk\u2010Type Iterative Schemes","display_name":"On the Rate of Convergence of Kirk\u2010Type Iterative Schemes","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2149820609","doi":"https://doi.org/10.1155/2012/526503","mag":"2149820609"},"language":"en","primary_location":{"id":"doi:10.1155/2012/526503","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/526503","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/526503.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/526503.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089045945","display_name":"Nawab Hussain","orcid":"https://orcid.org/0000-0001-6585-2202"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Nawab Hussain","raw_affiliation_strings":["Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054706815","display_name":"Renu Chugh","orcid":"https://orcid.org/0009-0003-5389-9304"},"institutions":[{"id":"https://openalex.org/I905734797","display_name":"Maharshi Dayanand University","ror":"https://ror.org/03kaab451","country_code":"IN","type":"education","lineage":["https://openalex.org/I905734797"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Renu Chugh","raw_affiliation_strings":["Department of Mathematics, M. D. University, Rohtak 124001, India","Department of Mathematics, M. D. University, Rohtak 124001"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, M. D. University, Rohtak 124001, India","institution_ids":["https://openalex.org/I905734797"]},{"raw_affiliation_string":"Department of Mathematics, M. D. University, Rohtak 124001","institution_ids":["https://openalex.org/I905734797"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018868633","display_name":"Vivek Kumar","orcid":"https://orcid.org/0000-0002-0274-5212"},"institutions":[{"id":"https://openalex.org/I905734797","display_name":"Maharshi Dayanand University","ror":"https://ror.org/03kaab451","country_code":"IN","type":"education","lineage":["https://openalex.org/I905734797"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vivek Kumar","raw_affiliation_strings":["Department of Mathematics, M. D. University, Rohtak 124001, India","Department of Mathematics, M. D. University, Rohtak 124001"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, M. D. University, Rohtak 124001, India","institution_ids":["https://openalex.org/I905734797"]},{"raw_affiliation_string":"Department of Mathematics, M. D. University, Rohtak 124001","institution_ids":["https://openalex.org/I905734797"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050635243","display_name":"Arif Rafiq","orcid":"https://orcid.org/0000-0003-0552-210X"},"institutions":[{"id":"https://openalex.org/I269276261","display_name":"Hajvery University","ror":"https://ror.org/01d6nwa88","country_code":"PK","type":"education","lineage":["https://openalex.org/I269276261"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Arif Rafiq","raw_affiliation_strings":["Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan","Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore"],"affiliations":[{"raw_affiliation_string":"Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan","institution_ids":["https://openalex.org/I269276261"]},{"raw_affiliation_string":"Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore","institution_ids":["https://openalex.org/I269276261"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089045945"],"corresponding_institution_ids":["https://openalex.org/I185163786"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":6.2197,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.96977729,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/sublinear-function","display_name":"Sublinear function","score":0.7419247627258301},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.648979663848877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6298913359642029},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.6112020611763},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5621384382247925},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5123552083969116},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47512727975845337},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.43117645382881165},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3326302170753479},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3021070957183838},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2869655191898346},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14305293560028076},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.056466370820999146}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.7419247627258301},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.648979663848877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6298913359642029},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6112020611763},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5621384382247925},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5123552083969116},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47512727975845337},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.43117645382881165},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3326302170753479},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3021070957183838},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2869655191898346},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14305293560028076},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.056466370820999146},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/526503","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/526503","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/526503.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1355495226","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495226","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:526503","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/526503.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:cf4e4b2f14c348439e8159a177813d56","is_oa":true,"landing_page_url":"https://doaj.org/article/cf4e4b2f14c348439e8159a177813d56","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":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/526503","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/526503","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/526503.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322322","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2149820609.pdf","grobid_xml":"https://content.openalex.org/works/W2149820609.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W27836280","https://openalex.org/W91175940","https://openalex.org/W1480205328","https://openalex.org/W1972091945","https://openalex.org/W1977108262","https://openalex.org/W1979507740","https://openalex.org/W1988600113","https://openalex.org/W1996239470","https://openalex.org/W2012066174","https://openalex.org/W2023358569","https://openalex.org/W2033060656","https://openalex.org/W2045471945","https://openalex.org/W2069435104","https://openalex.org/W2079711316","https://openalex.org/W2088536270","https://openalex.org/W2097091236","https://openalex.org/W2144971691","https://openalex.org/W2405271589","https://openalex.org/W2430129196","https://openalex.org/W2547907641","https://openalex.org/W4285719527","https://openalex.org/W4291439952","https://openalex.org/W6647372550","https://openalex.org/W6990113188"],"related_works":["https://openalex.org/W2945629716","https://openalex.org/W4283775266","https://openalex.org/W4298860769","https://openalex.org/W3043533097","https://openalex.org/W3007770227","https://openalex.org/W2767126220","https://openalex.org/W2351377961","https://openalex.org/W1942228078","https://openalex.org/W2086942802","https://openalex.org/W4385270631"],"abstract_inverted_index":{"The":[0],"purpose":[1],"of":[2,22,49,65],"this":[3],"paper":[4],"is":[5],"to":[6,18],"introduce":[7],"Kirk\u2010type":[8],"new":[9],"iterative":[10,24,44,61],"schemes":[11,16,25,45,62],"called":[12],"Kirk\u2010SP":[13],"and":[14,17,42,70],"Kirk\u2010CR":[15],"study":[19],"the":[20,59],"convergence":[21],"these":[23],"by":[26],"employing":[27],"certain":[28],"quasi\u2010contractive":[29],"operators.":[30,50],"By":[31],"taking":[32],"an":[33],"example,":[34],"we":[35,57],"will":[36],"compare":[37,58],"Kirk\u2010SP,":[38],"Kirk\u2010CR,":[39],"Kirk\u2010Mann,":[40],"Kirk\u2010Ishikawa,":[41],"Kirk\u2010Noor":[43],"for":[46],"aforementioned":[47],"class":[48],"Also,":[51],"using":[52],"computer":[53],"programs":[54],"in":[55],"C++,":[56],"above\u2010mentioned":[60],"through":[63],"examples":[64],"increasing,":[66],"decreasing,":[67],"sublinear,":[68],"superlinear,":[69],"oscillatory":[71],"functions.":[72]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}