The purpose of this paper is to introduce the Mandelbrot and Julia sets by using Picard-
Mann iteration procedure. Escape criteria is established which plays an important role to …

Fractals are a common characteristic of many artificial and natural networks having
topological patterns of a self-similar nature. For example, the Mandelbrot set has been …

In this paper, we generate some non-classical variants of Julia and Mandelbrot sets, utilizing
the Jungck-Ishikawa fixed point iteration system equipped with s-convexity. We establish a …

We show that an invariant Fatou component of a hyperbolic transcendental entire function is
a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points …

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 …

In recent years, researchers have studied the use of different iteration processes from fixed
point theory for the generation of complex fractals. Examples are the Mann, the Ishikawa, the …

Building on recent work by Rippon and Stallard, we explore the intricate structure of the
spider's web fast esca** sets associated with certain transcendental entire functions. Our …

We investigate some topological properties of Julia components, that is, connected
components of the Julia set, of a transcendental entire function f with a multiply-connected …

We show that if the Julia set of a transcendental entire function is locally connected, then it
takes the form of a spider's web in the sense defined by Rippon and Stallard. In the opposite …

Mandelbrot set is one of the most fascinating objects in mathematics, so in the literature, one
can find many studies related to this set. Moreover, there are many different extensions and …