{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T17:36:41Z","timestamp":1769103401104,"version":"3.49.0"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2021J01540"],"award-info":[{"award-number":["2021J01540"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2021J05106"],"award-info":[{"award-number":["2021J05106"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62176244"],"award-info":[{"award-number":["62176244"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LZ20F030001"],"award-info":[{"award-number":["LZ20F030001"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["621762404"],"award-info":[{"award-number":["621762404"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:p> As we know, feedforward neural networks (FNNs) with sigmoidal activation function are universal approximators. Theoretically, for any continuous function defined on a compact set, there exists an FNN such that the FNN can approximate the function with arbitrary accuracy, which constitutes a theoretical guarantee that FNN can be used as an efficient learning machine. This paper addresses the construction and approximation for FNNs. We construct an FNN with sigmoidal activation function and estimate its approximation error. In particular, an inverse theorem of the approximation is established, which implies the equivalence characterization theorem of the approximation and reveals the relationship between the topological structure of the FNN and its approximation ability. As keys in this study, the concepts of modulus of continuity of function, K-functional, and their relationship are utilized, and two Bernstein-type inequalities are established. <\/jats:p>","DOI":"10.1142\/s0219691323500285","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T04:05:30Z","timestamp":1683259530000},"source":"Crossref","is-referenced-by-count":5,"title":["Construction and approximation for a class of feedforward neural networks with sigmoidal function"],"prefix":"10.1142","volume":"21","author":[{"given":"Xinhong","family":"Meng","sequence":"first","affiliation":[{"name":"School of Electronics and Communication Engineering, Quanzhou University of Information Engineering, Quanzhou 362000, Fujian Province, P.\u00a0R.\u00a0China"}]},{"given":"Jinyao","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Electronics and Communication Engineering, Quanzhou University of Information Engineering, Quanzhou 362000, Fujian Province, P.\u00a0R.\u00a0China"}]},{"given":"Hailiang","family":"Ye","sequence":"additional","affiliation":[{"name":"College of Sciences, China Jiliang University, Hangzhou 310018, Zhejiang Province, P. 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