SAMS Subject Classification Number: 11

Iterated function systems are based on the mathematical foundations laid by Hutchinson [1]. He showed that Hutchinson operator constructed with the help of a finite system of contraction mappings defined on a Euclidean space \(% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n}\) has closed and bounded subset of \(% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n}\) as its fixed point, called attractor of iterated function system (see also in [2]). In this context, fixed point theory plays significant and vital role to help in the construction of fractals.

The aim of this talk is to present the sufficient conditions for the existence of attractor of a generalized cyclic iterated function system composed of a complete metric space and a finite family of generalized cyclic contraction mappings. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature [3,4].

[1] J. Hutchinson, Fractals and self-similarity, Indiana Univ. J. Math., 1981, 30 (5), 713-747.

[2] M. F. Barnsley, Fractals Everywhere, 2nd ed., Academic Press, San Diego, CA (1993).

[3] T. Nazir, M. Khumalo, V. Makhoshi, Iterated function system of generalized contractions in partial metric spaces, FILOMAT, 35:15 (2021), 201-220.

[4] M. Khumalo, T. Nazir and V. Makhoshi, Generalized iterated function system for common attractors in partial metric spaces, AIMS Mathematics, 7 (7) (2022), 13074-13103.