000084215 001__ 84215 000084215 005__ 20191212102141.0 000084215 0247_ $$2doi$$a10.1142/S0218348X18500792 000084215 0248_ $$2sideral$$a108578 000084215 037__ $$aART-2018-108578 000084215 041__ $$aeng 000084215 100__ $$0(orcid)0000-0003-4847-0493$$aNavascués, M.A.$$uUniversidad de Zaragoza 000084215 245__ $$aFractal approximation of Jackson type for periodic phenomena 000084215 260__ $$c2018 000084215 5060_ $$aAccess copy available to the general public$$fUnrestricted 000084215 5203_ $$aThe reconstruction of an unknown function providing a set of Lagrange data can be approached by means of fractal interpolation. The power of that methodology allows us to generalize any other interpolant, both smooth and nonsmooth, but the important fact is that this technique provides one of the few methods of nondifferentiable interpolation. In this way, it constitutes a functional model for chaotic processes. This paper studies a generalization of an approximation formula proposed by Dunham Jackson, where a wider range of values of an exponent of the basic trigonometric functions is considered. The trigonometric polynomials are then transformed in close fractal functions that, in general, are not smooth. For suitable election of this parameter, one obtains better conditions of convergence than in the classical case: the hypothesis of continuity alone is enough to ensure the convergence when the sampling frequency is increased. Finally, bounds of discrete fractal Jackson operators and their classical counterparts are proposed. 000084215 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000084215 590__ $$a2.971$$b2018 000084215 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b15 / 105 = 0.143$$c2018$$dQ1$$eT1 000084215 591__ $$aMULTIDISCIPLINARY SCIENCES$$b18 / 69 = 0.261$$c2018$$dQ2$$eT1 000084215 592__ $$a0.556$$b2018 000084215 593__ $$aApplied Mathematics$$c2018$$dQ1 000084215 593__ $$aMultidisciplinary$$c2018$$dQ1 000084215 593__ $$aModeling and Simulation$$c2018$$dQ1 000084215 593__ $$aGeometry and Topology$$c2018$$dQ1 000084215 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000084215 700__ $$aJha, S. 000084215 700__ $$aChand, A.K.B. 000084215 700__ $$0(orcid)0000-0002-0477-835X$$aSebastián, M.V. 000084215 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000084215 773__ $$g26, 5 (2018), 1850079 [14 pp]$$pFractals-Complex Geom. Patterns Scaling Nat. Soc.$$tFRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY$$x0218-348X 000084215 8564_ $$s311289$$uhttps://zaguan.unizar.es/record/84215/files/texto_completo.pdf$$yPostprint 000084215 8564_ $$s37795$$uhttps://zaguan.unizar.es/record/84215/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000084215 909CO $$ooai:zaguan.unizar.es:84215$$particulos$$pdriver 000084215 951__ $$a2019-12-12-10:12:15 000084215 980__ $$aARTICLE