Kantorovich-Bernstein a-fractal function in LP spaces

Chand, A.K.B. ; Jha, S. ; Navascués, M.A. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.2989/16073606.2019.1572664

Año: 2019

Publicado en: Quaestiones Mathematicae 43, 2 (2019), 227 - 241
ISSN: 1607-3606

Factor impacto JCR: 1.049 (2019)

Categ. JCR: MATHEMATICS rank: 105 / 324 = 0.324 (2019) - Q2 - T1

Factor impacto SCIMAGO: 0.364 - Mathematics (miscellaneous) (Q3)

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)