Parameter identification of constrained data by a new class of rational fractal function

This paper sets a theoretical foundation for the applications of fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with quadratic denominator involving two shape parameters. The elements iterated function system (IFS) in each subinterval are identified befittingly so that graph resulting $\mathcal{C}^1$-RCSFIF lies within prescribed rectangle. These parameters include, particular, conditions on positivity $\mathcal{C}^1$-RCSFIF. problem visualization constrained data is also addressed when lying above straight line, proposed curve required to lie same side line. illustrate our scheme some numerical examples