{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T15:53:31Z","timestamp":1786031611778,"version":"3.56.0"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T00:00:00Z","timestamp":1744329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we introduce and investigate the concept of statistical derivatives within the framework of the deferred Ces\u00e0ro summability technique, supported by illustrative examples. Using this approach, we establish a novel Korovkin-type theorem for a specific set of exponential test functions, namely 1, e\u2212\u03c5 and e\u22122\u03c5, which are defined on the Banach space C[0,\u221e). Our results significantly extend several well-known Korovkin-type theorems. Additionally, we analyze the rate of convergence associated with the statistical derivatives under deferred Ces\u00e0ro summability. To support our theoretical findings, we provide compelling numerical examples, followed by graphical representations generated using MATLAB software, to visually illustrate and enhance the understanding of the convergence behavior of the operators.<\/jats:p>","DOI":"10.3390\/a18040218","type":"journal-article","created":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T03:45:23Z","timestamp":1744343123000},"page":"218","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Korovkin-Type Theorems for Positive Linear Operators Based on the Statistical Derivative of Deferred Ces\u00e0ro Summability"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari Mohan","family":"Srivastava","sequence":"first","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":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan"},{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6776-0993","authenticated-orcid":false,"given":"Bidu Bhusan","family":"Jena","sequence":"additional","affiliation":[{"name":"Faculty of Science (Mathematics), Sri Sri University, Cuttack 754006, Odisha, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4465-7621","authenticated-orcid":false,"given":"Susanta Kumar","family":"Paikray","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Veer Surendra Sai University of Technology, Sambalpur 768018, Odisha, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Umakanta","family":"Misra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Science and Technology, Berhampur 761008, Odisha, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,11]]},"reference":[{"key":"ref_1","unstructured":"Ruddine, W. 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