000150553 001__ 150553 000150553 005__ 20251017144647.0 000150553 0247_ $$2doi$$a10.1016/j.chaos.2024.115883 000150553 0248_ $$2sideral$$a142632 000150553 037__ $$aART-2025-142632 000150553 041__ $$aeng 000150553 100__ $$0(orcid)0000-0003-4847-0493$$aNavascués, M.A. 000150553 245__ $$aNew algorithms for the approximation of fixed points and fractal functions 000150553 260__ $$c2025 000150553 5203_ $$aThis article is devoted to explore the abilities of an iterative scheme for the approximation of fixed points of self-maps, called the N-algorithm, defined in a previous paper. In a first part of the article, the algorithm is modified in order to consider operators with asymptotic properties, namely nearly uniform contractions and nearly asymptotically nonexpansive mappings. Sufficient conditions on the (normed or quasi-normed) underlying space and the operator are given in order to ensure weak or strong convergence of the new algorithm to a fixed point. Afterwards, the definition of fractal functions as fixed points of the Read-Bajraktarević operator is considered, giving very general conditions for their existence when the operator is nonexpansive. This is done in the framework of the Hilbert space, where is a real compact interval. The capacity of the N-algorithm for the approximation of these fractal functions is proved as well. In the last part of the paper, the fractal convolution of operators on is studied. The text explores the properties of the convolution when its components satisfy determined conditions, closely related to the existence of fixed points. 000150553 540__ $$9info:eu-repo/semantics/closedAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000150553 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000150553 773__ $$g191 (2025), 115883 [8 pp.]$$pChaos, solitons fractals$$tChaos, Solitons and Fractals$$x0960-0779 000150553 8564_ $$s945586$$uhttps://zaguan.unizar.es/record/150553/files/texto_completo.pdf$$yVersión publicada 000150553 8564_ $$s2522161$$uhttps://zaguan.unizar.es/record/150553/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000150553 909CO $$ooai:zaguan.unizar.es:150553$$particulos$$pdriver 000150553 951__ $$a2025-10-17-14:34:37 000150553 980__ $$aARTICLE