Construction of Fractal Functions Using Kannan Mappings and Smoothness Analysis
Abstract
Let T be a self-map on a metric space (X, d). Then T is called the Kannan map if there exists \alpha, 0 < \alpha < 1/2, such that d(T(x), T(y)) <= \alpha[d(x, T(x)) + d(y, T(y))], for all x, y in X. This paper aims to introduce a new method to construct fractal functions using Kannan mappings. First, we give the rigorous construction of fractal functions with the help of the Kannan iterated function system (IFS). We also show the existence of a Borel probability measure supported on the attractor of the Kannan IFS satisfying the strong separation condition. Moreover, we study the smoothness of the constructed fractal functions. We end the paper with some examples and graphical illustrations.
Keywords
Cite
@article{arxiv.2301.03075,
title = {Construction of Fractal Functions Using Kannan Mappings and Smoothness Analysis},
author = {Subhash Chandra and Saurabh Verma and Syed Abbas},
journal= {arXiv preprint arXiv:2301.03075},
year = {2024}
}
Comments
The readers are requested to not use the results of the current incomplete version as there are some issues in this. We will post the updated version soon