Shape preserving α-fractal rational cubic splines

In this article, a new alpha-fractal rational cubic spline is introduced with the help of the iterated function system (IFS) that contains rational functions. The numerator of the rational function contains a cubic polynomial and the denominator of the rational function contains a quadratic polynomial with three shape parameters. The convergence analysis of the alpha-fractal rational cubic spline is established. By restricting the scaling factors and the shape parameters, the alpha-fractal rational cubic spline is constrained between two piecewise linear functions whenever interpolation data lies in between two piecewise linear functions. Also, positivity and monotonicity of the alpha -fractal rational cubic spline are discussed. Numerical examples are provided to support the theoretical results.