Coupled fractals in complete metric spaces
Articles
Adrian Petru¸sel
Babe¸s-Bolyai University, Romania
Anna Soós
Academy of Romanian Scientists
Published 2018-04-12
https://doi.org/10.15388/NA.2018.2.1
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Keywords

set-to-set operator
fixed point
self-similar set
coupled fixed point
collage theorem

How to Cite

Petru¸sel A. and Soós A. (2018) “Coupled fractals in complete metric spaces”, Nonlinear Analysis: Modelling and Control, 23(2), pp. 141-158. doi: 10.15388/NA.2018.2.1.

Abstract

The aim of this paper is to present fixed set theorems, collage type and anticollage type results for single-valued operators T : X × X → X in the framework of a complete metric space X. Based on the coupled fixed point theory, existence of fixed sets, collage type and anticollage type results for iterated function systems are also presented. The results are closely related to self-similar sets theory and the mathematics of fractals. Several examples of coupled fractals illustrate our results.

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