{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:52:41Z","timestamp":1760057561200,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T00:00:00Z","timestamp":1739145600000},"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>We continue the studies of derivatives of the non-harmonic series \u2211cnexp(i\u03bbnx). We consider replacing sin\u03bbnx with some step function fn:[0,1)\u2192{0,1,2}. The purpose of this paper is to show that f(x)=\u2211fn(x)2n is continuous and nowhere differentiable in (0,1). All functions fn, used to construct f, are created from symmetrical blocks of type M: [0,1,0] and blocks of type L: [0,1,2] and R: [2,1,0], located symmetrically with respect to M. The function f1 takes the value zero in the intervals [0,1\/3), [2\/3,1) and the value one in the interval [1\/3,2\/3), i.e., it consists of the block of type M: [0,1,0]. Function f2 takes the value two in the intervals [2\/9,3\/9) and [6\/9,7\/9); the value one in the intervals [1\/9,2\/9), [4\/9,5\/9), and [7\/9,8\/9); and the value zero in the remaining intervals. This means a composition of blocks of [0,1,2][0,1,0][2,1,0], i.e., LMR blocks. The function f3 is a symmetric composition of blocks, LLMLMRMRR. These blocks are discontinuous analogs of the functions that produces Schoenberg curves.<\/jats:p>","DOI":"10.3390\/sym17020269","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T06:43:07Z","timestamp":1739169787000},"page":"269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Note on the Continuous and Nowhere Differentiable Function"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8195-779X","authenticated-orcid":false,"given":"Sergiusz","family":"K\u0119ska","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Faculty of Exact and Natural Sciences, University of Siedlce, 08-110 Siedlce, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,10]]},"reference":[{"key":"ref_1","first-page":"214","article-title":"The uniform convergence of a certain class of trigonometric series","volume":"15","author":"Chaundy","year":"1916","journal-title":"Proc. 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Continuous Nowhere Differentiable Functions, the Monster of Analysis, Springer.","DOI":"10.1007\/978-3-319-12670-8"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/269\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:30:26Z","timestamp":1760027426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/269"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,10]]},"references-count":12,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020269"],"URL":"https:\/\/doi.org\/10.3390\/sym17020269","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,2,10]]}}}