1. Kantorovich-Bernstein α-fractal function in P spaces.
- Author
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Chand, A.K.B., Jha, Sangita, and Navascués, M.A.
- Subjects
FUNCTION spaces ,LIPSCHITZ spaces ,FRACTALS ,INTERPOLATION - Abstract
Fractal interpolation functions are fixed points of contraction maps on suitable function spaces. In this paper, we introduce the Kantorovich-Bernstein α-fractal operator in the Lebesgue space
p (I), 1 ≤ p ≤ ∞. The main aim of this article is to study the convergence of the sequence of Kantorovich-Bernstein fractal functions towards the original functions inp (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 fractalp (I) functions from a given function in the same space. The existence of a Schauder basis consisting of self-referential functions inp spaces is proven. Further, we derive the fractal analogues of somep (I) approximation results, for example, the fractal version of the classical Müntz-Jackson theorem. The one-sided approximation by the Bernstein α-fractal function is developed. [ABSTRACT FROM AUTHOR]- Published
- 2020
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