150553 20251017144647.0 doi 10.1016/j.chaos.2024.115883 sideral 142632 ART-2025-142632 eng Navascués, M.A. (orcid)0000-0003-4847-0493 New algorithms for the approximation of fixed points and fractal functions 2025 This article is devoted to explore the abilities of an iterative scheme for the approximation of fixed points of self-maps, called the N-algorithm, defined in a previous paper. In a first part of the article, the algorithm is modified in order to consider operators with asymptotic properties, namely nearly uniform contractions and nearly asymptotically nonexpansive mappings. Sufficient conditions on the (normed or quasi-normed) underlying space and the operator are given in order to ensure weak or strong convergence of the new algorithm to a fixed point. Afterwards, the definition of fractal functions as fixed points of the Read-Bajraktarević operator is considered, giving very general conditions for their existence when the operator is nonexpansive. This is done in the framework of the Hilbert space, where is a real compact interval. The capacity of the N-algorithm for the approximation of these fractal functions is proved as well. In the last part of the paper, the fractal convolution of operators on is studied. The text explores the properties of the convolution when its components satisfy determined conditions, closely related to the existence of fixed points. info:eu-repo/semantics/closedAccess All rights reserved http://www.europeana.eu/rights/rr-f/ info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 191 (2025), 115883 [8 pp.] Chaos, solitons fractals Chaos, Solitons and Fractals 0960-0779 945586 http://zaguan.unizar.es/record/150553/files/texto_completo.pdf Versión publicada 2522161 http://zaguan.unizar.es/record/150553/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:150553 articulos driver 2025-10-17-14:34:37 ARTICLE