Fixed point results for fractal generation in Noor orbit and s-convexity

Springerplus. 2016 Oct 21;5(1):1843. doi: 10.1186/s40064-016-3530-5. eCollection 2016.

Abstract

In this note, we give fixed point results in fractal generation (Julia sets and Mandelbrot sets) by using Noor iteration scheme with s-convexity. Researchers have already presented fixed point results in Mann and Ishikawa orbits that are examples of one-step and two-step feedback processes respectively. In this paper we present fixed point results in Noor orbit, which is a three-step iterative procedure.

Keywords: Julia set; Mandelbrot set; Noor orbit; S-convexity.