{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T16:22:27Z","timestamp":1786033347905,"version":"3.56.0"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,9,16]],"date-time":"2021-09-16T00:00:00Z","timestamp":1631750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.<\/jats:p>","DOI":"10.3390\/axioms10030229","type":"journal-article","created":{"date-parts":[[2021,9,16]],"date-time":"2021-09-16T21:38:12Z","timestamp":1631828292000},"page":"229","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems"],"prefix":"10.3390","volume":"10","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":"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bidu Bhusan","family":"Jena","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, 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, Burla 768018, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"241","DOI":"10.4064\/cm-2-3-4-241-244","article-title":"Sur la convergence statistique","volume":"2","author":"Fast","year":"1951","journal-title":"Colloq. 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