SHAPE PRESERVING RATIONAL QUARTIC FRACTAL FUNCTIONS

Abstract

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 [Formula: see text]-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 [Formula: see text]-fractal rational quartic spline when the original function is in [Formula: see text]. By solving a system of linear equations, appropriate values of the derivative parameters are determined so as to enhance the continuity of the [Formula: see text]-fractal rational quartic spline to [Formula: see text]. The elements of the iterated function system are identified befittingly so that the class of [Formula: see text]-fractal function [Formula: see text] incorporates the geometric features such as positivity, monotonicity and convexity in addition to the regularity inherent in the germ [Formula: see text]. This general theory in conjunction with shape preserving aspects of the traditional splines provides algorithms for the construction of shape preserving fractal interpolation functions.