{"id":"https://openalex.org/W4380142864","doi":"https://doi.org/10.3390/sym15061169","title":"Some q-Symmetric Integral Inequalities Involving s-Convex Functions","display_name":"Some q-Symmetric Integral Inequalities Involving s-Convex Functions","publication_year":2023,"publication_date":"2023-05-29","ids":{"openalex":"https://openalex.org/W4380142864","doi":"https://doi.org/10.3390/sym15061169"},"language":"en","primary_location":{"id":"doi:10.3390/sym15061169","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15061169","pdf_url":"https://www.mdpi.com/2073-8994/15/6/1169/pdf?version=1685497075","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/2073-8994/15/6/1169/pdf?version=1685497075","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014358969","display_name":"Ammara Nosheen","orcid":"https://orcid.org/0000-0002-1627-4503"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ammara Nosheen","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1627-4503","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092130982","display_name":"Sana Ijaz","orcid":null},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sana Ijaz","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065052393","display_name":"Khuram Ali Khan","orcid":"https://orcid.org/0000-0002-3468-2295"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Khuram Ali Khan","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3468-2295","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079958089","display_name":"Khalid Mahmood Awan","orcid":"https://orcid.org/0000-0001-8401-4407"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khalid Mahmood Awan","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039377037","display_name":"Marwan Ali Albahar","orcid":"https://orcid.org/0000-0003-3586-3423"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Marwan Ali Albahar","raw_affiliation_strings":["Department of Computer Science, Umm Al-Qura University, Mecca 24382, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-3586-3423","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Umm Al-Qura University, Mecca 24382, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061186627","display_name":"Mohammed Thanoon","orcid":"https://orcid.org/0000-0001-5780-9749"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohammed Thanoon","raw_affiliation_strings":["Department of Computer Science, Umm Al-Qura University, Mecca 24382, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5780-9749","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Umm Al-Qura University, Mecca 24382, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065052393"],"corresponding_institution_ids":["https://openalex.org/I160968435"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":8.6424,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.98684911,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"6","first_page":"1169","last_page":"1169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.9606000185012817,"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/mathematics","display_name":"Mathematics","score":0.7869747877120972},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5527262091636658},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5503085851669312},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5309455394744873},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49362337589263916},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4358980059623718},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4288439154624939},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3467143177986145},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08486604690551758},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07551771402359009}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7869747877120972},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5527262091636658},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5503085851669312},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5309455394744873},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49362337589263916},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4358980059623718},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4288439154624939},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3467143177986145},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08486604690551758},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07551771402359009},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15061169","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15061169","pdf_url":"https://www.mdpi.com/2073-8994/15/6/1169/pdf?version=1685497075","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:82d86db5b4584701b6e3620bfe859dd4","is_oa":false,"landing_page_url":"https://doaj.org/article/82d86db5b4584701b6e3620bfe859dd4","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 6, p 1169 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/6/1169/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15061169","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/sym15061169","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15061169","pdf_url":"https://www.mdpi.com/2073-8994/15/6/1169/pdf?version=1685497075","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6499999761581421}],"awards":[],"funders":[{"id":"https://openalex.org/F4320324047","display_name":"Umm Al-Qura University","ror":"https://ror.org/01xjqrm90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4380142864.pdf","grobid_xml":"https://content.openalex.org/works/W4380142864.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W165488893","https://openalex.org/W832700260","https://openalex.org/W1576960788","https://openalex.org/W1963574764","https://openalex.org/W1965158021","https://openalex.org/W2007120062","https://openalex.org/W2057652230","https://openalex.org/W2144711631","https://openalex.org/W2255820928","https://openalex.org/W2322767775","https://openalex.org/W2510611020","https://openalex.org/W2529427475","https://openalex.org/W2560344843","https://openalex.org/W2942436572","https://openalex.org/W2948213511","https://openalex.org/W2992533838","https://openalex.org/W3164667188","https://openalex.org/W3164806255","https://openalex.org/W3192617994","https://openalex.org/W4240644230","https://openalex.org/W4283582165","https://openalex.org/W4285797622","https://openalex.org/W6623273313","https://openalex.org/W6634592943","https://openalex.org/W6692180895","https://openalex.org/W6748902012","https://openalex.org/W6763336991"],"related_works":["https://openalex.org/W4383100562","https://openalex.org/W2142149766","https://openalex.org/W4320933213","https://openalex.org/W2788930696","https://openalex.org/W4206205240","https://openalex.org/W4224316538","https://openalex.org/W2277657541","https://openalex.org/W3023535395","https://openalex.org/W4294611394","https://openalex.org/W4387635768"],"abstract_inverted_index":{"The":[0,15,33],"q-symmetric":[1,24,34,68],"analogues":[2],"of":[3,36,67,82],"H\u00f6lder,":[4],"Minkowski,":[5],"and":[6],"power":[7],"mean":[8],"inequalities":[9,17,43,51],"are":[10,26,44,61,76],"presented":[11],"in":[12,40,70],"this":[13],"paper.":[14],"obtained":[16],"along":[18],"with":[19,64],"a":[20],"Montgomery":[21],"identity":[22],"involving":[23],"integrals":[25],"used":[27],"to":[28,78],"extend":[29],"some":[30,49],"Ostrowski-type":[31,42],"inequalities.":[32],"derivatives":[35],"the":[37,65,71,80,83],"functions":[38,54,60],"involved":[39],"these":[41],"convex":[45,53],"or":[46],"s-convex.":[47],"Moreover,":[48],"Hermite\u2013Hadamard":[50],"for":[52,58],"as":[55,57],"well":[56],"s-convex":[59],"also":[62],"acquired":[63],"help":[66],"calculus":[69],"present":[72],"work.":[73],"Some":[74],"examples":[75],"included":[77],"support":[79],"effectiveness":[81],"proved":[84],"results.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-06-10T00:00:00"}