Fixed point results for the complex fractal generation in the S -iteration orbit with s -convexity

Abstract

Since the introduction of complex fractals by Mandelbrot they gained much attention by the researchers. One of the most studied complex fractals are Mandelbrot and Julia sets. In the literature one can find many generalizations of those sets. One of such generalizations is the use of the results from fixed point theory. In this paper we introduce in the generation process of Mandelbrot and Julia sets a combination of the S-iteration, known from the fixed point theory, and the s-convex combination. We derive the escape criteria needed in the generation process of those fractals and present some graphical examples.