{"id":"https://openalex.org/W4366588653","doi":"https://doi.org/10.3390/sym15040937","title":"On Some Bounds for the Gamma Function","display_name":"On Some Bounds for the Gamma Function","publication_year":2023,"publication_date":"2023-04-19","ids":{"openalex":"https://openalex.org/W4366588653","doi":"https://doi.org/10.3390/sym15040937"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040937","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040937","pdf_url":"https://www.mdpi.com/2073-8994/15/4/937/pdf?version=1681902860","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/2073-8994/15/4/937/pdf?version=1681902860","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024058768","display_name":"Mansour Mahmoud","orcid":"https://orcid.org/0000-0002-5918-1913"},"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":"Mansour Mahmoud","raw_affiliation_strings":["Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5918-1913","affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031123999","display_name":"Saud M. Alsulami","orcid":"https://orcid.org/0000-0002-4833-753X"},"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":false,"raw_author_name":"Saud M. Alsulami","raw_affiliation_strings":["Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-4833-753X","affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038356501","display_name":"Safiah Almarashi","orcid":null},"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":false,"raw_author_name":"Safiah Almarashi","raw_affiliation_strings":["Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024058768"],"corresponding_institution_ids":["https://openalex.org/I185163786"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.0349,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84661428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"15","issue":"4","first_page":"937","last_page":"937"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9731000065803528,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9319999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7578976154327393},{"id":"https://openalex.org/keywords/gamma-function","display_name":"Gamma function","score":0.5991512537002563},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5863516926765442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5612673759460449},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5232816338539124},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5153219103813171},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4831111431121826},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4692383110523224},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46256953477859497},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32925522327423096},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21057233214378357},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0583251416683197}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7578976154327393},{"id":"https://openalex.org/C82240120","wikidata":"https://www.wikidata.org/wiki/Q190573","display_name":"Gamma function","level":2,"score":0.5991512537002563},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5863516926765442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5612673759460449},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5232816338539124},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5153219103813171},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4831111431121826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4692383110523224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46256953477859497},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32925522327423096},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21057233214378357},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0583251416683197},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040937","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040937","pdf_url":"https://www.mdpi.com/2073-8994/15/4/937/pdf?version=1681902860","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:c49a44e26a1340aeb28a60bb5118f8d6","is_oa":false,"landing_page_url":"https://doaj.org/article/c49a44e26a1340aeb28a60bb5118f8d6","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 4, p 937 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/937/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040937","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/sym15040937","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040937","pdf_url":"https://www.mdpi.com/2073-8994/15/4/937/pdf?version=1681902860","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":[{"id":"https://metadata.un.org/sdg/10","score":0.5199999809265137,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4366588653.pdf"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W655236323","https://openalex.org/W1967505091","https://openalex.org/W1991737430","https://openalex.org/W2035518722","https://openalex.org/W2057475195","https://openalex.org/W2058704243","https://openalex.org/W2063935787","https://openalex.org/W2073098195","https://openalex.org/W2090174767","https://openalex.org/W2153531485","https://openalex.org/W2329241700","https://openalex.org/W2563037548","https://openalex.org/W2893486885","https://openalex.org/W2894812057","https://openalex.org/W2963575702","https://openalex.org/W2963715022","https://openalex.org/W4236996230","https://openalex.org/W4299584580","https://openalex.org/W4309710726","https://openalex.org/W6696410271"],"related_works":["https://openalex.org/W2950472823","https://openalex.org/W2081972949","https://openalex.org/W3103046732","https://openalex.org/W1761810493","https://openalex.org/W3021649813","https://openalex.org/W2949622191","https://openalex.org/W4287808774","https://openalex.org/W3098325605","https://openalex.org/W3106530133","https://openalex.org/W1499397612"],"abstract_inverted_index":{"Both":[0],"theoretical":[1],"and":[2],"applied":[3],"mathematics":[4],"depend":[5],"heavily":[6],"on":[7,22],"inequalities,":[8],"which":[9],"are":[10,59],"rich":[11],"in":[12],"symmetries.":[13],"In":[14,33],"numerous":[15],"studies,":[16],"estimations":[17],"of":[18,25,40,53,56],"various":[19],"functions":[20,42],"based":[21],"the":[23,38,54],"characteristics":[24],"their":[26],"symmetry":[27],"have":[28],"been":[29],"provided":[30],"through":[31],"inequalities.":[32,66],"this":[34],"paper,":[35],"we":[36],"study":[37],"monotonicity":[39],"certain":[41],"that":[43,58],"involve":[44],"Gamma":[45],"functions.":[46],"We":[47],"were":[48],"able":[49],"to":[50],"obtain":[51],"some":[52,63],"bounds":[55],"\u0393(v)":[57],"more":[60],"accurate":[61],"than":[62],"recently":[64],"published":[65]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}