{"id":"https://openalex.org/W2058120896","doi":"https://doi.org/10.1016/s0893-9659(03)90015-2","title":"Convolutions for special classes of harmonic univalent functions","display_name":"Convolutions for special classes of harmonic univalent functions","publication_year":2003,"publication_date":"2003-08-01","ids":{"openalex":"https://openalex.org/W2058120896","doi":"https://doi.org/10.1016/s0893-9659(03)90015-2","mag":"2058120896"},"language":"en","primary_location":{"id":"doi:10.1016/s0893-9659(03)90015-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0893-9659(03)90015-2","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051057235","display_name":"Om P. Ahuja","orcid":"https://orcid.org/0000-0003-0701-6390"},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"O.P. Ahuja","raw_affiliation_strings":["Department of Mathematical Sciences, Kent State University 14111 Clairdon Troy Raod, Burton, OH 544201-9500, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Kent State University 14111 Clairdon Troy Raod, Burton, OH 544201-9500, U.S.A","institution_ids":["https://openalex.org/I149910238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068794336","display_name":"Jay M. Jahangiri","orcid":"https://orcid.org/0000-0002-5231-3530"},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J.M. Jahangiri","raw_affiliation_strings":["Department of Mathematical Sciences, Kent State University 14111 Clairdon Troy Raod, Burton, OH 544201-9500, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Kent State University 14111 Clairdon Troy Raod, Burton, OH 544201-9500, U.S.A","institution_ids":["https://openalex.org/I149910238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018795962","display_name":"Herb Silverman","orcid":null},"institutions":[{"id":"https://openalex.org/I204593131","display_name":"College of Charleston","ror":"https://ror.org/00390t168","country_code":"US","type":"education","lineage":["https://openalex.org/I204593131"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"H. Silverman","raw_affiliation_strings":["College of Charleston 66 George Street, Charleston, SC 29424, U.S.A"],"affiliations":[{"raw_affiliation_string":"College of Charleston 66 George Street, Charleston, SC 29424, U.S.A","institution_ids":["https://openalex.org/I204593131"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018795962","https://openalex.org/A5051057235","https://openalex.org/A5068794336"],"corresponding_institution_ids":["https://openalex.org/I149910238","https://openalex.org/I204593131"],"apc_list":{"value":3540,"currency":"USD","value_usd":3540},"apc_paid":null,"fwci":0.4501,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.61041617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"6","first_page":"905","last_page":"909"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","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/T11822","display_name":"Analytic and geometric function theory","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8573755621910095},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.7793064117431641},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6961979866027832},{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.6619640588760376},{"id":"https://openalex.org/keywords/hadamard-product","display_name":"Hadamard product","score":0.6543805003166199},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6131426692008972},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.5749038457870483},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.523414134979248},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4962669014930725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.460246741771698},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4591275155544281},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.44953563809394836},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4347188472747803},{"id":"https://openalex.org/keywords/convolution-power","display_name":"Convolution power","score":0.4129115641117096},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4126240015029907},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.3822416663169861},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.07983258366584778},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06682828068733215},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.057775139808654785}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8573755621910095},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.7793064117431641},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6961979866027832},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.6619640588760376},{"id":"https://openalex.org/C90230998","wikidata":"https://www.wikidata.org/wiki/Q3406746","display_name":"Hadamard product","level":3,"score":0.6543805003166199},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6131426692008972},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.5749038457870483},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.523414134979248},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4962669014930725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.460246741771698},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4591275155544281},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.44953563809394836},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4347188472747803},{"id":"https://openalex.org/C86254553","wikidata":"https://www.wikidata.org/wiki/Q5166605","display_name":"Convolution power","level":5,"score":0.4129115641117096},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4126240015029907},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.3822416663169861},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.07983258366584778},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06682828068733215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.057775139808654785},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0893-9659(03)90015-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0893-9659(03)90015-2","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1988126813","https://openalex.org/W1992487348","https://openalex.org/W2030301675","https://openalex.org/W2037289103","https://openalex.org/W2084822343","https://openalex.org/W6646986956"],"related_works":["https://openalex.org/W2929896563","https://openalex.org/W2096222268","https://openalex.org/W2326484792","https://openalex.org/W2328262823","https://openalex.org/W2081084069","https://openalex.org/W2184884434","https://openalex.org/W4229442126","https://openalex.org/W2741386133","https://openalex.org/W2058120896","https://openalex.org/W2060722394"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}