000120176 001__ 120176 000120176 005__ 20240319081013.0 000120176 0247_ $$2doi$$a10.3390/fractalfract6120722 000120176 0248_ $$2sideral$$a131069 000120176 037__ $$aART-2022-131069 000120176 041__ $$aeng 000120176 100__ $$0(orcid)0000-0003-4847-0493$$aNavascués Sanagustín, María Antonia$$uUniversidad de Zaragoza 000120176 245__ $$aFractal curves on Banach algebras 000120176 260__ $$c2022 000120176 5060_ $$aAccess copy available to the general public$$fUnrestricted 000120176 5203_ $$aMost of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as Banach spaces and algebras, with minimal conditions and structures, transcending in this way the numerical underlying scenario. This is performed via fixed point of an operator defined on a b-metric space of Banach-valued functions with domain on a real interval. The sets of images may provide uniparametric fractal collections of measures, operators or matrices, for instance. The defining operator is linked to a collection of maps (or iterated function system, and the conditions on these mappings determine the properties of the fractal function. In particular, it is possible to define continuous curves and fractal functions belonging to Bochner spaces of Banach-valued integrable functions. As residual result, we prove the existence of fractal functions coming from non-contractive operators as well. We provide new constructions of bases for Banach-valued maps, with a particular mention of spanning systems of functions valued on C*-algebras. 000120176 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000120176 590__ $$a5.4$$b2022 000120176 592__ $$a0.627$$b2022 000120176 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b9 / 107 = 0.084$$c2022$$dQ1$$eT1 000120176 593__ $$aAnalysis$$c2022$$dQ2 000120176 593__ $$aStatistics and Probability$$c2022$$dQ2 000120176 593__ $$aStatistical and Nonlinear Physics$$c2022$$dQ2 000120176 594__ $$a3.6$$b2022 000120176 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000120176 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000120176 773__ $$g6, 12 (2022), 722 [17 pp.]$$pFractal fract.$$tFractal and fractional$$x2504-3110 000120176 8564_ $$s344494$$uhttps://zaguan.unizar.es/record/120176/files/texto_completo.pdf$$yVersión publicada 000120176 8564_ $$s2431681$$uhttps://zaguan.unizar.es/record/120176/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000120176 909CO $$ooai:zaguan.unizar.es:120176$$particulos$$pdriver 000120176 951__ $$a2024-03-18-15:21:54 000120176 980__ $$aARTICLE