{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T07:57:00Z","timestamp":1762070220870,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T00:00:00Z","timestamp":1665187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003093","name":"Ministry of Higher Education","doi-asserted-by":"publisher","award":["FRGS\/1\/2020\/STG06\/SYUC\/02\/1"],"award-info":[{"award-number":["FRGS\/1\/2020\/STG06\/SYUC\/02\/1"]}],"id":[{"id":"10.13039\/501100003093","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein generalization is established. It is also shown that the Cheney\u2013Sharma operator is the Sz\u00e1sz\u2013Mirakyan operator averaged by a certain probability distribution.<\/jats:p>","DOI":"10.3390\/axioms11100537","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T20:43:21Z","timestamp":1665261801000},"page":"537","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Some Probabilistic Generalizations of the Cheney\u2013Sharma and Bernstein Approximation Operators"],"prefix":"10.3390","volume":"11","author":[{"given":"Seng Huat","family":"Ong","sequence":"first","affiliation":[{"name":"Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia"},{"name":"Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0157-2732","authenticated-orcid":false,"given":"Choung Min","family":"Ng","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3350-3993","authenticated-orcid":false,"given":"Hong Keat","family":"Yap","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Kajang 43000, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari Mohan","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,8]]},"reference":[{"key":"ref_1","unstructured":"Szeg\u00f6, G. 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