New Fixed Point Results for Fractal Generation in Jungck Noor Orbit withs-Convexity

Abstract

We establish new fixed point results in the generation of fractals (Julia sets, Mandelbrot sets, and Tricorns and Multicorns for linear or nonlinear dynamics) by using Jungck Noor iteration withs-convexity.

Generation of New Fractals via SP Orbit with s-Convexity

“…Recently, M. Kumari et al [16] used a new iterative process (an example of four-step feedback process) for creating new Julia and Mandelbrot sets for quadratic, cubic and higher degree polynomials. Further, some researchers obtained fixed point results in the generation of Julia and Mandelbrot sets with s-convexity, see ( [15], [22], [28]).…”

The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings

“…e result presented in this paper plays crucial theoretical base of the numerical analysis for nonlinear problems which are often encountered in physical and biological sciences. e future direction for this paper is to determine for the class of asymptotically nonexpansive mappings and the conditions for the convergence of Jungck Noor iteration with s-convexity, defined by Kang et al [2] and to compare the rate of convergence with the implicit midpoint procedure.…”

Generation of Julia and Mandelbrot Sets via Fixed Points

“…It is noteworthy that for each iterative process the behaviour and dynamics of the Julia and Mandelbrot sets differ. For some thought-provoking and fascinating comparisons, the reader may refer to [1,24,[27][28][29] and references therein.…”

“…Kang et al [28] introduced Julia and Mandelbrot sets in implicit Jungck Mann and Jungck Ishikawa orbits. Later, several researchers [27,29,[31][32][33] employed this implicit iterative process to generate graphs of such complex polynomials. In order to achieve this, they split the polynomial T into two functions T 1 (x) = x n + r and T 2 (x) = mx.…”