Stability, Data Dependence, and Convergence Results with Computational Engendering of Fractals via Jungck–DK Iterative Scheme

Abstract

We have developed a Jungck version of the DK iterative scheme called the Jungck–DK iterative scheme. Our analysis focuses on the convergence and stability of the Jungck–DK scheme for a pair of non-self-mappings using the more general contractive condition. We demonstrate that this iterative scheme converges faster than all other leading Jungck-type iterative schemes. To further illustrate its effectiveness, we provide an example to verify the rate of convergence and prove the data dependence result for the Jungck–DK iterative scheme. Finally, we calculate the escape criteria for generating Mandelbrot and Julia sets for polynomial functions and present visually appealing images of these sets by our modified iteration.

Keywords

• Jungck–DK scheme
• contraction mapping
• Banach space
• stability
• data dependence
• fractals