New Julia and Mandelbrot Sets for Jungck Ishikawa Iterates

Abstract

The generation of fractals and study of the dynamics of polynomials is one of the emerging and interesting field of research nowadays. We introduce in this paper the dynamics of polynomials z^ n - z + c = 0 for n>=2 and applied Jungck Ishikawa Iteration to generate new Relative Superior Mandelbrot sets and Relative Superior Julia sets. In order to solve this function by Jungck type iterative schemes, we write it in the form of Sz = Tz, where the function T, S are defined as Tz = z^ n + c and Sz = z. Only mathematical explanations are derived by applying Jungck Ishikawa Iteration for polynomials in the literature but in this paper we have generated Relative Mandelbrot sets and Relative Julia sets.