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Such functions appear widely in PDE, probability law distributions, statistical modeling, etc. Some of the most known approximators nowadays are neural networks and wavelets, which constitute good classes of elementary functions permitting as efficiently as possible to describe functions in appropriate spaces. This paper aims to develop combined neural networks and wavelet approximators for functions, based on the involvement of wavelets as activation functions. Some necessary conditions on the activation function to approximate [Formula: see text] and [Formula: see text]-elements are relaxed as well as those on the measure [Formula: see text]. We prove that for a wavelet activation function, any element of [Formula: see text] as well as [Formula: see text] can be well approximated for arbitrary measures [Formula: see text]. The theoretical results are subject to an experimental application in order to show their effectiveness.<\/jats:p>","DOI":"10.1142\/s0219691321500600","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T11:01:51Z","timestamp":1638183711000},"source":"Crossref","is-referenced-by-count":10,"title":["Wavelet neural networks functional approximation and application"],"prefix":"10.1142","volume":"20","author":[{"given":"Anis","family":"Zeglaoui","sequence":"first","affiliation":[{"name":"MaPSFA-ESST Hammam Sousse, University of Sousse, 4011 Sousse, Tunisia"},{"name":"Ecole Nationale d\u2019Ing\u00e9nieurs de Sousse, University of Sousse, 4023 Sousse, Tunisia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2571-1066","authenticated-orcid":false,"given":"Anouar","family":"Ben Mabrouk","sequence":"additional","affiliation":[{"name":"Laboratory of Algebra, Number Theory and Nonlinear Analysis LR15ES18, Department of Mathematics, Faculty of Sciences, University of Monastir, 5000 Monastir, Tunisia"},{"name":"Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, Street of Assad Ibn Alfourat, University of Kairouan, 3100 Kairouan, Tunisia"},{"name":"Department of Mathematics, College of Sciences, University of Tabuk, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oleg V.","family":"Kravchenko","sequence":"additional","affiliation":[{"name":"Dorodnicyn Computing Centre, FRC CSC RAS, Bauman Moscow State Technical University, Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2022,3,8]]},"reference":[{"issue":"7","key":"S0219691321500600BIB001","first-page":"1","volume":"10","author":"Khalek M. 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