Invited Speaker
Dr. Talat Nazir
Department of Mathematical Sciences, Universiy of South Africa, Florida Campus, South AfricaSpeech Title: Iterated Function System of Generalized Hutchinson Operators for Global Fractals
Abstract: Iterated function systems are based on the mathematical foundations laid by Hutchin-son [1]. He showed that Hutchinson operator constructed with the help of a Önite system of contraction mappings deÖned on a Euclidean space Rn has closed and bounded subset of Rn as its Öxed point, called attractor of iterated function system (see also in [2] ). In this context, Öxed point theory plays signiÖcant and vital role to help in the construction of fractals.
The aim of this talk is to present the su¢ cient conditions for the existence of attractor of a generalized iterated function system composed of a complete metric space and a Önite family of generalized contractive mappings. Some examples are presented for construction of global fractals to support our main results presented therein. The results obtained in the presentation extend and generalize various well known results in the existing literature [3, 4].
References
[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.