Quantum alpha-fractal approximation

Vijender, N. ; Chand, A.K.B. ; Navascues, M.A. (Universidad de Zaragoza) ; Sebastian, M.V.

Resumen: Fractal approximation is a well studied concept, but the convergence of all the existing fractal approximants towards the original function follows usually if the magnitude of the corresponding scaling factors approaches zero. In this article, for a given functionf is an element of C(I), by exploiting fractal approximation theory and considering the classicalq-Bernstein polynomials asbase functions, we construct a sequence{fn(q, alpha)(x)}n=1 infinity of(q, alpha)-fractal functions that converges uniformly tofeven if the norm/magnitude of the scaling functions/scaling factors does not tend to zero. The convergence of the sequence{fn(q, alpha)(x)}n=1 infinity of(q, alpha)-fractal functions towardsffollows from the convergence of the sequence ofq-Bernstein polynomials offtowardsf. If we consider a sequence{fm(x)}m=1 infinity of positive functions on a compact real interval that converges uniformly to a functionf, we develop a double sequence{{fm, n(q, alpha)(x)}n=1 infinity}m=1 infinity of(q, alpha)-fractal functions that converges uniformly tof.

Idioma: Inglés

DOI: 10.1080/00207160.2020.1792449

Año: 2021

Publicado en: International journal of computer mathematics 98, 12 (2021), 2355-2368
ISSN: 0020-7160

Factor impacto JCR: 1.75 (2021)

Categ. JCR: MATHEMATICS, APPLIED rank: 99 / 267 = 0.371 (2021) - Q2 - T2

Factor impacto CITESCORE: 3.4 - Mathematics (Q1) - Computer Science (Q2)

Factor impacto SCIMAGO: 0.519 - Computer Science Applications (Q2) - Applied Mathematics (Q2)

Tipo y forma: Article (PostPrint)

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