Shape Preserving Rational Quartic Fractal Functions

The appearance of fractal interpolation function represents a revival of experimental mathematics, raised by computers and intensified by powerful evidence of its applications. This paper is devoted to establish a method to construct α-fractal rational quartic spline, which eventually provides a unified approach for the generalization of various traditional nonrecursive rational splines involving shape parameters. We deduce the uniform error bound for the α-fractal rational quartic spline when the original function is in 4(I). By solving a system of linear equations, appropriate values of the derivative parameters are determined so as to enhance the continuity of the α-fractal rational quartic spline to 2. The elements of the iterated function system are identified befittingly so that the class of α-fractal function Qα incorporates the geometric features such as positivity, monotonicity and convexity in addition to the regularity inherent in the germ Q. This general theory in conjunction with shape preserving aspects of the traditional splines provides algorithms for the construction of shape preserving fractal interpolation functions.