{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T20:15:53Z","timestamp":1780517753852,"version":"3.54.1"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,3,31]],"date-time":"2019-03-31T00:00:00Z","timestamp":1553990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The concept of statistically deferred-weighted summability was recently studied by Srivastava et al. (Math. Methods Appl. Sci. 41 (2018), 671\u2013683). The present work is concerned with the deferred-weighted summability mean in various aspects defined over a modular space associated with a generalized double sequence of functions. In fact, herein we introduce the idea of relatively modular deferred-weighted statistical convergence and statistically as well as relatively modular deferred-weighted summability for a double sequence of functions. With these concepts and notions in view, we establish a theorem presenting a connection between them. Moreover, based upon our methods, we prove an approximation theorem of the Korovkin type for a double sequence of functions on a modular space and demonstrate that our theorem effectively extends and improves most (if not all) of the previously existing results. Finally, an illustrative example is provided here by the generalized bivariate Bernstein\u2013Kantorovich operators of double sequences of functions in order to demonstrate that our established theorem is stronger than its traditional and statistical versions.<\/jats:p>","DOI":"10.3390\/sym11040448","type":"journal-article","created":{"date-parts":[[2019,4,2]],"date-time":"2019-04-02T03:21:26Z","timestamp":1554175286000},"page":"448","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Statistically and Relatively Modular Deferred-Weighted Summability and Korovkin-Type Approximation Theorems"],"prefix":"10.3390","volume":"11","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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bidu Bhusan","family":"Jena","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha 768018, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Susanta Kumar","family":"Paikray","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha 768018, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Umakanta","family":"Misra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Science and Technology, Palur Hills, Golanthara, Odisha 761008, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,31]]},"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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