Some results on the space of rational cubic fractal interpolation functions

In this article, rational cubic fractal interpolation function (RCFIF) with three shape parameters is constructed. We develope the orthonormal basis consists of cardinal RCFIFs for the space of RCFIFs with fixed parameters. We show the space RCFIFs with fixed parameters is a reproducing kernel Hilbert space and we study the curve fitting problem. Also, we discuss the orthogonal projection on the space of RCFIFs with fixed parameters. Further, we study the constrained aspects of cardinal RCFIFs. Numerical results are provided to support theoretical results.