000119823 001__ 119823 000119823 005__ 20240319081005.0 000119823 0247_ $$2doi$$a10.3390/fractalfract6100602 000119823 0248_ $$2sideral$$a130659 000119823 037__ $$aART-2022-130659 000119823 041__ $$aeng 000119823 100__ $$0(orcid)0000-0003-4847-0493$$aNavascués, María A.$$uUniversidad de Zaragoza 000119823 245__ $$aScale-free fractal interpolation 000119823 260__ $$c2022 000119823 5060_ $$aAccess copy available to the general public$$fUnrestricted 000119823 5203_ $$aAn iterated function system that defines a fractal interpolation function, where ordinate scaling is replaced by a nonlinear contraction, is investigated here. In such a manner, fractal interpolation functions associated with Matkowski contractions for finite as well as infinite (countable) sets of data are obtained. Furthermore, we construct an extension of the concept of α-fractal interpolation functions, herein called R-fractal interpolation functions, related to a finite as well as to a countable iterated function system and provide approximation properties of the R-fractal functions. Moreover, we obtain smooth R-fractal interpolation functions and provide results that ensure the existence of differentiable R-fractal interpolation functions both for the finite and the infinite (countable) cases. 000119823 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000119823 590__ $$a5.4$$b2022 000119823 592__ $$a0.627$$b2022 000119823 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b9 / 107 = 0.084$$c2022$$dQ1$$eT1 000119823 593__ $$aAnalysis$$c2022$$dQ2 000119823 593__ $$aStatistics and Probability$$c2022$$dQ2 000119823 593__ $$aStatistical and Nonlinear Physics$$c2022$$dQ2 000119823 594__ $$a3.6$$b2022 000119823 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000119823 700__ $$aPacurar, Cristina 000119823 700__ $$aDrakopoulos, Vasileios 000119823 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000119823 773__ $$g6, 10 (2022), 602 [15 pp]$$pFractal fract.$$tFractal and fractional$$x2504-3110 000119823 8564_ $$s358862$$uhttps://zaguan.unizar.es/record/119823/files/texto_completo.pdf$$yVersión publicada 000119823 8564_ $$s2689769$$uhttps://zaguan.unizar.es/record/119823/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000119823 909CO $$ooai:zaguan.unizar.es:119823$$particulos$$pdriver 000119823 951__ $$a2024-03-18-14:31:41 000119823 980__ $$aARTICLE