Boundaries of Filled Julia Sets in Generalized Jungck Mann Orbit

In this paper, we study the generalized Jungck Mann orbit (GJMO) and prove the converse theorem of results. We develop algorithms for the generation of filled Julia sets and their boundaries in the GJMO. In simple Julia set (i.e., boundary of filled Julia set), we show the internal structure of Julia set and establish the correspondence between Julia points via dark blue lines in graphs. Moreover, we demonstrate the pictorial effects of filled Julia set and its boundary and graphically present the image change with the change of complex parameter
$c$
in the GJMO.