New algorithms for the approximation of fixed points and fractal functions

M.A. Navascués

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: 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.

Keywords: Asymptotically nonexpansive and contractive maps; Fixed point approximation; α-fractal functions; Fractal convolution; Iterative methods (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014358

DOI: 10.1016/j.chaos.2024.115883

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