The Picard–Mann iteration with s-convexity in the generation of Mandelbrot and Julia sets

Abstract In recent years, researchers have studied the use of different iteration processes from fixed point theory in generation complex fractals. For instance, Mann, Ishikawa, Noor, Jungck–Mann and Jungck–Ishikawa iterations been used. this paper, we study Picard–Mann with s -convexity Mandelbrot Julia sets. We prove escape criterion for $$(k+1)$$ ( k + 1 ) st degree polynomial. Moreover, present some graphical numerical examples regarding sets generated using proposed iteration.