{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:24Z","timestamp":1740134544008,"version":"3.37.3"},"reference-count":38,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>The limit -Bernstein operator emerges naturally as a modification of the Sz\u00e1sz-Mirakyan operator related to the Euler distribution, which is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplary model for the study of the convergence of the -operators. Over the past years, the limit -Bernstein operator has been studied widely from different perspectives. It has been shown that is a positive shape-preserving linear operator on with . Its approximation properties, probabilistic interpretation, the behavior of iterates, and the impact on the smoothness of a function have already been examined. In this paper, we present a review of the results on the limit -Bernstein operator related to the approximation theory. A complete bibliography is supplied.<\/jats:p>","DOI":"10.1155\/2013\/159720","type":"journal-article","created":{"date-parts":[[2013,3,28]],"date-time":"2013-03-28T17:03:16Z","timestamp":1364490196000},"page":"1-7","source":"Crossref","is-referenced-by-count":3,"title":["A Survey of Results on the Limit -Bernstein Operator"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0447-4591","authenticated-orcid":true,"given":"Sofiya","family":"Ostrovska","sequence":"first","affiliation":[{"name":"Department of Mathematics, Atilim University, Ankara 06836, 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