000088443 001__ 88443 000088443 005__ 20200716101505.0 000088443 0247_ $$2doi$$a10.2989/16073606.2019.1572664 000088443 0248_ $$2sideral$$a111533 000088443 037__ $$aART-2019-111533 000088443 041__ $$aeng 000088443 100__ $$aChand, A.K.B. 000088443 245__ $$aKantorovich-Bernstein a-fractal function in LP spaces 000088443 260__ $$c2019 000088443 5060_ $$aAccess copy available to the general public$$fUnrestricted 000088443 5203_ $$aFractal 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. 000088443 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000088443 590__ $$a1.049$$b2019 000088443 591__ $$aMATHEMATICS$$b105 / 324 = 0.324$$c2019$$dQ2$$eT1 000088443 592__ $$a0.364$$b2019 000088443 593__ $$aMathematics (miscellaneous)$$c2019$$dQ3 000088443 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000088443 700__ $$aJha, S. 000088443 700__ $$0(orcid)0000-0003-4847-0493$$aNavascués, M.A.$$uUniversidad de Zaragoza 000088443 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000088443 773__ $$g43, 2 (2019), 227 - 241$$pQuaest. math. (Grahamst., Print)$$tQuaestiones Mathematicae$$x1607-3606 000088443 8564_ $$s476190$$uhttps://zaguan.unizar.es/record/88443/files/texto_completo.pdf$$yPostprint 000088443 8564_ $$s251909$$uhttps://zaguan.unizar.es/record/88443/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000088443 909CO $$ooai:zaguan.unizar.es:88443$$particulos$$pdriver 000088443 951__ $$a2020-07-16-09:15:29 000088443 980__ $$aARTICLE