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We construct a generalized C r-Fractal Interpolation Function (C r-FIF) f by prescribing any combination of r values of the derivatives f (k) , k = 1, 2,. .. , r, at boundary points of the interval I = [x 0 , x N ]. Our approach to construction settles several questions of Barnsley and Harrington [J. Approx Theory, 57 (1989), pp. 14–34] when construction is… (More)

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