In this paper, we introduce and investigate some definition and property of self-similar group and strong self-similar group of Kannan contraction. These groups are found as the attractor of a Kannan iterated function system (KIFS). This paper improves the Hutchinson-Barnsley theory in the sense of KIFS. Fractal set can be constructed by self-similar and strong self-similar group in the sense of KIFS of compact topological group. Finally, we prove the relation between profinite group and strong self-similar group of Kannan contraction.
Uthayakumar, R. and Gowrisankar, A.
"Generation of Fractals via Self-Similar Group of Kannan Iterated Function System,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 52.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss6/52