 Fractals of two types of enriched (q,θ)-Hutchinson–Barnsley operatorsRizwan Anjum, Muhammad Din and Mi Zhou Chaos, Solitons & Fractals, 2024, vol. 181, issue C Abstract: The aim of this paper is to introduce and develop two novel classifications of enriched (q,θ)-contractions on Banach spaces. The paper includes illustrative examples to demonstrate these concepts and establishes the convergence of Krasnoselskii’s iteration method when applied to approximate the fixed point of such enriched (q,θ)-contractions. Additionally, the paper explores the application of these concepts in constructing the fractals of the corresponding Hutchinson–Barnsley operators. The above construction is illustrated by some examples. These discoveries provide new fixed-point solutions for iterated function systems under various contractive conditions. Finally, as an application of our main result, the existence of the solution to the problem of fourth order differential equation is presented. Furthermore, the findings not only validate but also enhance and expand upon multiple established conclusions in the existing literature. Keywords: (generalized) enriched (q,θ)-contractions; Krasnoselskii’s iteration; Hutchinson–Barnsley operator; (generalized) enriched (q, θ)-iterated function system; Fractals (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001401 DOI: 10.1016/j.chaos.2024.114589 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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