Complex Dynamics of Sine Function using Jungck Ishikawa Iterates

The dynamics of transcendental function is one of emerging and interesting field of research nowadays. We introduce in this paper the complex dynamics of sine function of the type {sin (zn ) - z + c = 0} and applied Jungck Ishikawa iteration to generate Relative Superior Mandelbrot set and Relative Superior Julia set. 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 = sin ( zn ) +c and Sz= z. Only mathematical explanations are derived by applying Jungck Ishikawa Iteration for transcendental function in the literature but in this paper we have generated relative Mandelbrot sets and Relative Julia sets.