{"doi":"10.3390/sym13101919","title":"On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter λ","abstract":"<jats:p>This paper deals with several approximation properties for a new class of q-Bernstein polynomials based on new Bernstein basis functions with shape parameter λ on the symmetric interval [−1,1]. Firstly, we computed some moments and central moments. Then, we constructed a Korovkin-type convergence theorem, bounding the error in terms of the ordinary modulus of smoothness, providing estimates for Lipschitz-type functions. Finally, with the aid of Maple software, we present the comparison of the convergence of these newly constructed polynomials to the certain functions with some graphical illustrations and error estimation tables.</jats:p>","journal":"Symmetry","year":2021,"id":23082,"datarank":1.577695894810523,"base_score":3.5553480614894135,"endowment":3.5553480614894135,"self_citation_contribution":0.5333022092234121,"citation_network_contribution":1.044393685587111,"self_endowment_contribution":0.5333022092234121,"citer_contribution":1.044393685587111,"corpus_percentile":null,"corpus_rank":null,"citation_count":34,"citer_count":19,"citers_with_citation_signal":15,"citers_with_endowment":15,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":142977,"name":"Reşat Aslan","orcid":"0000-0002-8180-9199","position":1,"is_corresponding":false},{"id":142976,"name":"Qing-Bo Cai","orcid":"0000-0003-4759-7441","position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":3.5553480614894135,"endowment":3.5553480614894135,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21071399","pmcid":null,"openalex_id":"https://openalex.org/W3206709119","authors":[],"funders":[{"funder_name":"Natural Science Foundation of Fujian Province of China","grant_id":"2020J01783","title":null},{"funder_name":"Project for High-level Talent Innovation and Entrepreneurship of 116 Quanzhou","grant_id":"2018C087R","title":null}],"total_grants":2,"fwci":5.8437,"citation_percentile":0.97305649,"influential_citations":0,"citation_trend":[{"year":2022,"count":13},{"year":2023,"count":6},{"year":2024,"count":6},{"year":2025,"count":7},{"year":2026,"count":2}],"oa_status":"gold","license":"cc-by","oa_locations":[{"url":"https://www.mdpi.com/2073-8994/13/10/1919/pdf?version=1634107482","host_type":"journal"},{"url":"https://www.mdpi.com/2073-8994/13/10/1919/pdf?version=1634107482","host_type":"GOLD"},{"url":"https://www.mdpi.com/2073-8994/13/10/1919/pdf?version=1634107482","host_type":"publisher"},{"url":"https://www.mdpi.com/2073-8994/13/10/1919/pdf","host_type":"publisher"},{"url":"https://doi.org/10.3390/sym13101919","host_type":"journal"},{"url":"https://avesis.yyu.edu.tr/publication/details/883f096b-8bc1-4e13-a969-eee217a044a8/oai","host_type":"repository"},{"url":"https://doaj.org/article/f6421812461d49939eb1ed90dfb9e9b4","host_type":"repository"},{"url":"https://dx.doi.org/10.3390/sym13101919","host_type":"repository"}],"fields_of_study":["Approximation Theory and Sequence Spaces","Advanced Numerical Analysis Techniques","Iterative Methods for Nonlinear Equations","Computer Science","Mathematics"],"mesh_terms":[],"keywords":["Bernstein polynomial","Mathematics","Maple","Lipschitz continuity","Bounding overwatch","Convergence (economics)","Smoothness","Applied mathematics","Interval (graph theory)","Type (biology)","Pure mathematics","Mathematical analysis","Combinatorics","Computer science"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-07T17:56:06.658621Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}