{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T00:45:12Z","timestamp":1775522712401,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,26]],"date-time":"2025-01-26T00:00:00Z","timestamp":1737849600000},"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>This study introduces novel concepts of convergence and summability for numerical sequences, grounded in the newly formulated deferred N\u00f6rlund density, and explores their intrinsic connections to symmetry in mathematical structures. By leveraging symmetry principles inherent in sequence behavior and employing two distinct modulus functions under varying conditions, profound links between sequence convergence and summability are established. The study further incorporates lacunary refinements, enhancing the understanding of N\u00f6rlund statistical convergence and its symmetric properties. Key theorems, properties, and illustrative examples validate the proposed concepts, providing fresh insights into the role of symmetry in shaping broader convergence theories and advancing the understanding of sequence behavior across diverse mathematical frameworks.<\/jats:p>","DOI":"10.3390\/sym17020192","type":"journal-article","created":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T04:59:10Z","timestamp":1737953950000},"page":"192","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Exploring a Novel Approach to Deferred N\u00f6rlund Statistical Convergence"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9927-2388","authenticated-orcid":false,"given":"Ibrahim Sulaiman","family":"Ibrahim","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1636-0559","authenticated-orcid":false,"given":"Ji-Huan","family":"He","sequence":"additional","affiliation":[{"name":"School of Jia Yang, Zhejiang Shuren University, Hangzhou 310015, China"},{"name":"National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou 215123, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8833-6585","authenticated-orcid":false,"given":"Nejmeddine","family":"Chorfi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0206-3828","authenticated-orcid":false,"given":"Majeed Ahmad","family":"Yousif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq"},{"name":"Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel","family":"Vivas-Cortez","sequence":"additional","affiliation":[{"name":"Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de Octubre 1076 y Roca, Sede Quito 17-01-2184, Ecuador"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,26]]},"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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