{"id":"https://openalex.org/W3201654168","doi":"https://doi.org/10.3390/sym13091738","title":"A Variety of Dynamic Steffensen-Type Inequalities on a General Time Scale","display_name":"A Variety of Dynamic Steffensen-Type Inequalities on a General Time Scale","publication_year":2021,"publication_date":"2021-09-18","ids":{"openalex":"https://openalex.org/W3201654168","doi":"https://doi.org/10.3390/sym13091738","mag":"3201654168"},"language":"en","primary_location":{"id":"doi:10.3390/sym13091738","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091738","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1738/pdf?version=1632383262","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/2073-8994/13/9/1738/pdf?version=1632383262","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000462219","display_name":"Ahmed A. El\u2010Deeb","orcid":null},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Ahmed Abdel-Moneim El-Deeb","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt","institution_ids":["https://openalex.org/I184834183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034511816","display_name":"Omar Bazighifan","orcid":"https://orcid.org/0000-0002-7251-9608"},"institutions":[{"id":"https://openalex.org/I319841309","display_name":"Hadhramout University","ror":"https://ror.org/02kv0px94","country_code":"YE","type":"education","lineage":["https://openalex.org/I319841309"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT","YE"],"is_corresponding":false,"raw_author_name":"Omar Bazighifan","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen","Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7251-9608","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen","institution_ids":["https://openalex.org/I319841309"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025074757","display_name":"Jan Awrejcewicz","orcid":"https://orcid.org/0000-0003-0387-921X"},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Jan Awrejcewicz","raw_affiliation_strings":["Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland"],"raw_orcid":"https://orcid.org/0000-0003-0387-921X","affiliations":[{"raw_affiliation_string":"Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland","institution_ids":["https://openalex.org/I188884621"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000462219","https://openalex.org/A5025074757"],"corresponding_institution_ids":["https://openalex.org/I184834183","https://openalex.org/I188884621"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.641,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.90479371,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"13","issue":"9","first_page":"1738","last_page":"1738"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9958000183105469,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9958000183105469,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.993399977684021,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.5913435220718384},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.57625412940979},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5376490354537964},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.524341881275177},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5150720477104187},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.507243812084198},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.4822445809841156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45692017674446106},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4471834897994995},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3807827830314636},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3494720458984375},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3319286108016968},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28754857182502747},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11578309535980225},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09588634967803955},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09481441974639893},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.050636470317840576}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5913435220718384},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.57625412940979},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5376490354537964},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.524341881275177},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5150720477104187},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.507243812084198},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.4822445809841156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45692017674446106},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4471834897994995},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3807827830314636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3494720458984375},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3319286108016968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28754857182502747},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11578309535980225},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09588634967803955},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09481441974639893},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.050636470317840576},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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":3,"locations":[{"id":"doi:10.3390/sym13091738","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091738","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1738/pdf?version=1632383262","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:1eb6e284c3af49e7aa60dd821f4fcaec","is_oa":true,"landing_page_url":"https://doaj.org/article/1eb6e284c3af49e7aa60dd821f4fcaec","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":"Symmetry, Vol 13, Iss 9, p 1738 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/9/1738/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13091738","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/sym13091738","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091738","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1738/pdf?version=1632383262","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":[{"score":0.7200000286102295,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3201654168.pdf","grobid_xml":"https://content.openalex.org/works/W3201654168.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W98230489","https://openalex.org/W271810198","https://openalex.org/W1973067404","https://openalex.org/W2015450767","https://openalex.org/W2035495750","https://openalex.org/W2053075147","https://openalex.org/W2066397800","https://openalex.org/W2078828212","https://openalex.org/W2088959414","https://openalex.org/W2729088626","https://openalex.org/W2778421026","https://openalex.org/W2800962038","https://openalex.org/W2885350278","https://openalex.org/W2951581408","https://openalex.org/W2967156670","https://openalex.org/W3103061760","https://openalex.org/W6670217817","https://openalex.org/W6672692357"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W1539596337","https://openalex.org/W33469805","https://openalex.org/W1855007440","https://openalex.org/W2788247819","https://openalex.org/W2914699178","https://openalex.org/W2024985363","https://openalex.org/W4301243416","https://openalex.org/W2156911440","https://openalex.org/W4299682115"],"abstract_inverted_index":{"This":[0],"work":[1,6,16],"is":[2],"motivated":[3],"by":[4],"the":[5,15,22,25,37,66],"of":[7,17,24,36,50],"Josip":[8],"Pe\u010dari\u0107":[9],"in":[10,19,64],"2013":[11],"and":[12,14,39,44],"1982":[13],"Srivastava":[18],"2017.":[20],"By":[21],"utilization":[23],"diamond-\u03b1":[26,51],"dynamic":[27,71],"inequalities,":[28],"which":[29],"are":[30],"defined":[31],"as":[32],"a":[33,55],"linear":[34],"mixture":[35],"delta":[38],"nabla":[40],"integrals,":[41],"we":[42],"present":[43],"prove":[45],"very":[46],"important":[47],"generalized":[48],"results":[49],"Steffensen-type":[52],"inequalities":[53],"on":[54],"general":[56],"time":[57],"scale.":[58],"Symmetry":[59],"plays":[60],"an":[61],"essential":[62],"role":[63],"determining":[65],"correct":[67],"methods":[68],"to":[69],"solve":[70],"inequalities.":[72]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
