88443 20200716101505.0 doi 10.2989/16073606.2019.1572664 sideral 111533 ART-2019-111533 eng Chand, A.K.B. Kantorovich-Bernstein a-fractal function in LP spaces 2019 Access copy available to the general public Unrestricted Fractal interpolation functions are fixed points of contraction maps on suitable function spaces. In this paper, we introduce the Kantorovich-Bernstein a-fractal operator in the Lebesgue space Lp(I), 1 = p = 8. The main aim of this article is to study the convergence of the sequence of Kantorovich-Bernstein fractal functions towards the original functions in Lp(I) spaces and Lipschitz spaces without affecting the non-linearity of the fractal functions. In the first part of this paper, we introduce a new family of self-referential fractal Lp(I) functions from a given function in the same space. The existence of a Schauder basis consisting of self-referential functions in Lp spaces is proven. Further, we derive the fractal analogues of some Lp(I) approximation results, for example, the fractal version of the classical Müntz-Jackson theorem. The one-sided approximation by the Bernstein a-fractal function is developed. info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.049 2019 MATHEMATICS 105 / 324 = 0.324 2019 Q2 T1 0.364 2019 Mathematics (miscellaneous) 2019 Q3 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Jha, S. (orcid)0000-0003-4847-0493 Navascués, M.A. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 43, 2 (2019), 227 - 241 Quaest. math. (Grahamst., Print) Quaestiones Mathematicae 1607-3606 476190 http://zaguan.unizar.es/record/88443/files/texto_completo.pdf Postprint 251909 http://zaguan.unizar.es/record/88443/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:88443 articulos driver 2020-07-16-09:15:29 ARTICLE