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- W2918086562 abstract "Fractal interpolation functions defined by means of suitable Iterated Function Systemsprovide a new framework for the approximation of continuous functions defined on a compact real interval.Convergence is one of the desirable properties of a good approximant.The goal of the present paper is to develop fractal approximants, namelyBernstein $alpha$-fractal functions, which converge to the given continuous functioneven if the magnitude of the scaling factors does not approach zero.We use Bernstein $alpha$-fractal functions toconstruct the sequence of Bernstein Müntz fractal polynomials that converges toeither $fin mathcal{C}(I)$ or $fin L^p(I), 1 le p < infty.$ This gives afractal analogue of the full Müntz theorems in the aforementioned function spaces.For a given sequence ${f_n(x)}^{infty}_{n=1}$ of continuous functionsthat converges uniformly to a function $fin mathcal{C}(I),$ we developa double sequence $big{{f_{n,l}^{alpha}(x)}^infty_{l=1}big}^infty_{n=1}$ of Bernstein $alpha$-fractal functionsthat converges uniformly to $f$. By establishing suitable conditions on thescaling factors, we solve a constrained approximation problem of Bernstein $alpha$-fractal Müntz polynomials.We also study the convergence of Bernstein fractal Chebyshev series." @default.
- W2918086562 created "2019-03-02" @default.
- W2918086562 creator A5035133754 @default.
- W2918086562 date "2019-01-01" @default.
- W2918086562 modified "2023-10-17" @default.
- W2918086562 title "Bernstein fractal approximation and fractal full Müntz theorems" @default.
- W2918086562 doi "https://doi.org/10.1553/etna_vol51s1" @default.
- W2918086562 hasPublicationYear "2019" @default.
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