{"id":"https://openalex.org/W3043457708","doi":"https://doi.org/10.1155/2020/9307302","title":"Some Valid Generalizations of Boyd and Wong Inequality and<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>\u03c8</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03d5</mml:mi></mml:mrow></mml:mfenced></mml:math>-Weak Contraction in Partially Ordered<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mi>b</mml:mi><mml:mo>\u2212</mml:mo></mml:math>Metric Spaces","display_name":"Some Valid Generalizations of Boyd and Wong Inequality and<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>\u03c8</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03d5</mml:mi></mml:mrow></mml:mfenced></mml:math>-Weak Contraction in Partially Ordered<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mml:mi>b</mml:mi><mml:mo>\u2212</mml:mo></mml:math>Metric Spaces","publication_year":2020,"publication_date":"2020-07-13","ids":{"openalex":"https://openalex.org/W3043457708","doi":"https://doi.org/10.1155/2020/9307302","mag":"3043457708"},"language":"en","primary_location":{"id":"doi:10.1155/2020/9307302","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/9307302","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2020/9307302.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","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/ijmms/2020/9307302.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075264771","display_name":"Noor Jamal","orcid":"https://orcid.org/0009-0001-8029-8104"},"institutions":[{"id":"https://openalex.org/I68649149","display_name":"University of Malakand","ror":"https://ror.org/012xdha97","country_code":"PK","type":"education","lineage":["https://openalex.org/I68649149"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Noor Jamal","raw_affiliation_strings":["Department of Mathematics, University of Malakand, Chakdara, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Malakand, Chakdara, Pakistan","institution_ids":["https://openalex.org/I68649149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043412155","display_name":"Thabet Abdeljawad","orcid":"https://orcid.org/0000-0002-8889-3768"},"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"]},{"id":"https://openalex.org/I143578492","display_name":"Asia University","ror":"https://ror.org/038a1tp19","country_code":"TW","type":"education","lineage":["https://openalex.org/I143578492"]},{"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"]}],"countries":["SA","TW"],"is_corresponding":true,"raw_author_name":"Thabet Abdeljawad","raw_affiliation_strings":["Department Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia","Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan","Department of Medical Research, China Medical University, Taichung 40402, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]},{"raw_affiliation_string":"Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan","institution_ids":["https://openalex.org/I143578492"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076816198","display_name":"Muhammad Sarwar","orcid":"https://orcid.org/0000-0003-3904-8442"},"institutions":[{"id":"https://openalex.org/I68649149","display_name":"University of Malakand","ror":"https://ror.org/012xdha97","country_code":"PK","type":"education","lineage":["https://openalex.org/I68649149"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Sarwar","raw_affiliation_strings":["Department of Mathematics, University of Malakand, Chakdara, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Malakand, Chakdara, Pakistan","institution_ids":["https://openalex.org/I68649149"]}]},{"author_position":"middle","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 Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076381835","display_name":"Sumati Kumari Panda","orcid":"https://orcid.org/0000-0002-0220-8222"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panda Sumati Kumari","raw_affiliation_strings":["Department of Mathematics, GMR Institute of Technology, Rajam 532 127, Andhra Pradesh, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, GMR Institute of Technology, Rajam 532 127, Andhra Pradesh, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5043412155"],"corresponding_institution_ids":["https://openalex.org/I142024983","https://openalex.org/I143578492","https://openalex.org/I184693016"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.1682,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.77108099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"13"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9248999953269958,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5339720249176025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5153297781944275},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.45684751868247986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33104562759399414}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5339720249176025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5153297781944275},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.45684751868247986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33104562759399414},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2020/9307302","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/9307302","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2020/9307302.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a1313053bdc44fe89f6086f9ffcd9012","is_oa":true,"landing_page_url":"https://doaj.org/article/a1313053bdc44fe89f6086f9ffcd9012","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/9307302","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/9307302","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2020/9307302.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5850764610","display_name":null,"funder_award_id":"NAMAM","funder_id":"https://openalex.org/F4320327702","funder_display_name":"Prince Sultan University"},{"id":"https://openalex.org/G6468897384","display_name":null,"funder_award_id":"RG-DES-2017-01-17","funder_id":"https://openalex.org/F4320327702","funder_display_name":"Prince Sultan University"}],"funders":[{"id":"https://openalex.org/F4320327702","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3043457708.pdf","grobid_xml":"https://content.openalex.org/works/W3043457708.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1458771408","https://openalex.org/W1691516306","https://openalex.org/W1981459842","https://openalex.org/W1985195480","https://openalex.org/W1986350092","https://openalex.org/W1987583991","https://openalex.org/W1988476861","https://openalex.org/W2015222848","https://openalex.org/W2036759414","https://openalex.org/W2061914963","https://openalex.org/W2065421932","https://openalex.org/W2074766818","https://openalex.org/W2075540323","https://openalex.org/W2079622135","https://openalex.org/W2127777186","https://openalex.org/W2145364632","https://openalex.org/W2163562208","https://openalex.org/W2164303263","https://openalex.org/W2464825547","https://openalex.org/W2473587624","https://openalex.org/W2562964995","https://openalex.org/W2606502243","https://openalex.org/W2782694957","https://openalex.org/W2782818958","https://openalex.org/W2789550020","https://openalex.org/W2792400343","https://openalex.org/W2802962688","https://openalex.org/W2928693584","https://openalex.org/W2946225276","https://openalex.org/W2987700273","https://openalex.org/W2989881150","https://openalex.org/W2999404547","https://openalex.org/W4251578279"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596"],"abstract_inverted_index":{"In":[0],"this":[1],"manuscript,":[2],"we":[3],"use<mml:math":[4],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5],"id=\"M3\"><mml:mfenced":[6],"open=\"(\"":[7],"close=\")\"":[8],"separators=\"|\"><mml:mrow><mml:mi>\u03c8</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03d5</mml:mi></mml:mrow></mml:mfenced></mml:math>-weak":[9],"contraction":[10],"to":[11,44],"generalize":[12],"coincidence":[13],"point":[14],"results":[15,35],"which":[16],"are":[17,41],"established":[18,50],"in":[19],"the":[20,37,46,49],"context":[21],"of":[22,48],"partially":[23],"ordered":[24],"b":[25],"-metric":[26],"spaces.":[27],"The":[28],"presented":[29],"work":[30],"explicitly":[31],"generalized":[32],"some":[33],"recent":[34],"from":[36],"existing":[38],"literature.":[39],"Examples":[40],"also":[42],"provided":[43],"show":[45],"authenticity":[47],"work.":[51]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2020-07-23T00:00:00"}