{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T18:13:59Z","timestamp":1784916839619,"version":"3.55.0"},"reference-count":38,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T00:00:00Z","timestamp":1591056000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Lucian Blaga University of Sibiu &amp; Hasso Plattner Foundation","award":["LBUS-IRG-2019-05"],"award-info":[{"award-number":["LBUS-IRG-2019-05"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present paper, we deal with some general estimates for the difference of operators which are associated with different fundamental functions. In order to exemplify the theoretical results presented in (for example) Theorem 2, we provide the estimates of the differences between some of the most representative operators used in Approximation Theory in especially the difference between the Baskakov and the Sz\u00e1sz\u2013Mirakyan operators, the difference between the Baskakov and the Sz\u00e1sz\u2013Mirakyan\u2013Baskakov operators, the difference of two genuine-Durrmeyer type operators, and the difference of the Durrmeyer operators and the Lupa\u015f\u2013Durrmeyer operators. By means of illustrative numerical examples, we show that, for particular cases, our result improves the estimates obtained by using the classical result of Shisha and Mond. We also provide the symmetry aspects of some of these approximations operators which we have studied in this paper.<\/jats:p>","DOI":"10.3390\/sym12060915","type":"journal-article","created":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T04:12:09Z","timestamp":1591157529000},"page":"915","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Difference of Some Positive Linear Approximation Operators for Higher-Order Derivatives"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5768-5763","authenticated-orcid":false,"given":"Vijay","family":"Gupta","sequence":"first","affiliation":[{"name":"Department of Mathematics, Netaji Subhas University of Technology, Sector 3 Dwarka, New Delhi 110078, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1192-2281","authenticated-orcid":false,"given":"Ana Maria","family":"Acu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, R-550012 Sibiu, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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, AZ1007 Baku, Azerbaijan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yalcin, F., and Simsek, Y. (2020). A new class of symmetric Beta type distributions constructed by means of symmetric Bernstein type basis functions. 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