{"id":"https://openalex.org/W4386743750","doi":"https://doi.org/10.3390/sym15091755","title":"Shape Preserving Properties of Parametric Sz\u00e1sz Type Operators on Unbounded Intervals","display_name":"Shape Preserving Properties of Parametric Sz\u00e1sz Type Operators on Unbounded Intervals","publication_year":2023,"publication_date":"2023-09-13","ids":{"openalex":"https://openalex.org/W4386743750","doi":"https://doi.org/10.3390/sym15091755"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091755","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091755","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1755/pdf?version=1694605637","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/2073-8994/15/9/1755/pdf?version=1694605637","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100574451","display_name":"Hui Dong","orcid":null},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Dong","raw_affiliation_strings":["School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091009052","display_name":"Qiulan Qi","orcid":"https://orcid.org/0000-0002-2743-8622"},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qiulan Qi","raw_affiliation_strings":["Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, China","School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China"],"affiliations":[{"raw_affiliation_string":"Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, China","institution_ids":[]},{"raw_affiliation_string":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China","institution_ids":["https://openalex.org/I94611258"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091009052"],"corresponding_institution_ids":["https://openalex.org/I94611258"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0042,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.78123539,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"15","issue":"9","first_page":"1755","last_page":"1755"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9897000193595886,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9855999946594238,"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/operator","display_name":"Operator (biology)","score":0.6883677840232849},{"id":"https://openalex.org/keywords/modulus-of-continuity","display_name":"Modulus of continuity","score":0.6627278327941895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6496265530586243},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6137908101081848},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5697598457336426},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5631977915763855},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5372955799102783},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.4821895658969879},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.48018160462379456},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4737979769706726},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46019744873046875},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.43904542922973633},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.42506909370422363},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36301353573799133},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13587498664855957}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6883677840232849},{"id":"https://openalex.org/C3098717","wikidata":"https://www.wikidata.org/wiki/Q1144872","display_name":"Modulus of continuity","level":3,"score":0.6627278327941895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6496265530586243},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6137908101081848},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5697598457336426},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5631977915763855},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5372955799102783},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.4821895658969879},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.48018160462379456},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4737979769706726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46019744873046875},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.43904542922973633},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.42506909370422363},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36301353573799133},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13587498664855957},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym15091755","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091755","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1755/pdf?version=1694605637","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:163a2e104893465c8bbf1c10dd432ebb","is_oa":true,"landing_page_url":"https://doaj.org/article/163a2e104893465c8bbf1c10dd432ebb","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 9, p 1755 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15091755","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091755","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1755/pdf?version=1694605637","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":0.7099999785423279,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G6135491951","display_name":null,"funder_award_id":"L2020203","funder_id":"https://openalex.org/F4320321948","funder_display_name":"Hebei Normal University"}],"funders":[{"id":"https://openalex.org/F4320321948","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386743750.pdf","grobid_xml":"https://content.openalex.org/works/W4386743750.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1488909131","https://openalex.org/W1970922678","https://openalex.org/W1975853342","https://openalex.org/W1989203263","https://openalex.org/W1990553417","https://openalex.org/W2007311080","https://openalex.org/W2009467882","https://openalex.org/W2016553523","https://openalex.org/W2034759823","https://openalex.org/W2052391364","https://openalex.org/W2057192935","https://openalex.org/W2066403099","https://openalex.org/W2077011847","https://openalex.org/W2087880182","https://openalex.org/W2091259332","https://openalex.org/W2593549088","https://openalex.org/W4285008821","https://openalex.org/W4293203761","https://openalex.org/W4307829788","https://openalex.org/W6742199472"],"related_works":["https://openalex.org/W4254386783","https://openalex.org/W2940405130","https://openalex.org/W2363211409","https://openalex.org/W2376481828","https://openalex.org/W2964442496","https://openalex.org/W2390990501","https://openalex.org/W4244087063","https://openalex.org/W2035309570","https://openalex.org/W2002792507","https://openalex.org/W4226280031"],"abstract_inverted_index":{"The":[0],"Be\u00b4zier-type":[1],"operator":[2,9,31],"has":[3],"become":[4],"a":[5],"powerful":[6],"tool":[7],"in":[8,32],"theory,":[10],"neural":[11],"networks,":[12],"curve":[13],"and":[14,17,64,83,103],"surface":[15],"design":[16],"representation":[18],"because":[19],"of":[20,29,40,43,58,62,75,86,99],"its":[21],"good":[22],"shape-preserving":[23],"properties.":[24],"Motivated":[25],"by":[26],"the":[27,30,54,56,60,65,84,96,100,104],"improvements":[28],"computational":[33],"disciplines,":[34],"we":[35,69],"investigate":[36],"some":[37,71,89],"elementary":[38],"properties":[39,74],"two":[41],"kinds":[42],"modified":[44],"Sza\u00b4sz":[45],"type":[46],"basis":[47],"functions,":[48],"depending":[49],"on":[50],"non-negative":[51],"parameters.":[52],"Using":[53],"derivative,":[55],"symmetry":[57],"variables,":[59],"modulus":[61],"continuity":[63],"concave":[66],"continuous":[67],"modulus,":[68],"study":[70],"shape":[72],"preserving":[73],"these":[76],"operators":[77,102],"concerning":[78],"monotonicity,":[79],"convexity,":[80],"starshapedness,":[81],"semi-additivity":[82],"preservation":[85],"smoothness.":[87],"Moreover,":[88],"illustrative":[90],"examples":[91],"are":[92],"provided":[93],"to":[94],"demonstrate":[95],"approximation":[97],"behavior":[98],"proposed":[101],"classical":[105],"ones.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2023-09-15T00:00:00"}
