{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T18:00:46Z","timestamp":1785002446895,"version":"3.55.0"},"reference-count":46,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T00:00:00Z","timestamp":1633996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Fujian Province of China","award":["2020J01783"],"award-info":[{"award-number":["2020J01783"]}]},{"name":"Project for High-level Talent Innovation and Entrepreneurship of 116 Quanzhou","award":["2018C087R"],"award-info":[{"award-number":["2018C087R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"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 \u03bb on the symmetric interval [\u22121,1]. 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>","DOI":"10.3390\/sym13101919","type":"journal-article","created":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T21:48:39Z","timestamp":1634161719000},"page":"1919","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter \u03bb"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4759-7441","authenticated-orcid":false,"given":"Qing-Bo","family":"Cai","sequence":"first","affiliation":[{"name":"Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8180-9199","authenticated-orcid":false,"given":"Re\u015fat","family":"Aslan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts, Harran University, Haliliye 63300, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,12]]},"reference":[{"key":"ref_1","first-page":"85","article-title":"A q-analogue of the Bernstein operator","volume":"9","year":"1987","journal-title":"Semin. 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