Zipper Rational Quadratic Fractal Interpolation Functions

Inthis article, we propose an interpolation method using a binary parameter called signature such that the graph of the interpolant is an attractor of a suitable zipper rational iterated function system. The presence of scaling factors and signature in the proposed zipper rational quadratic fractal interpolation functions (ZRQFIFs) gives the flexibility to produce a wide variety of interpolants. Using suitable conditions on the scale factor and shape parameter, we construct a C1-continuous ZRQFIF from a C0-continuous ZRQFIF. We also establish the uniform convergence of ZRQFIF to an original data-generating function. Further, we deduce suitable conditions on the IFS parameters and shape parameters to retain the positivity feature associated with a prescribed data by the proposed interpolant.