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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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Volume 8, Issue 2

Issues

Volume 13 (2015)

Multivalued fractals in b-metric spaces

Monica Boriceanu / Marius Bota / Adrian Petruşel
Published Online: 2010-04-14 | DOI: https://doi.org/10.2478/s11533-010-0009-4

Abstract

Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.

MSC: 47H10; 54H25

Keywords: Multivalued operator; Fixed point; Strict fixed point; b-metric space; Self-similar set; Fractal operator; Multi-fractal operator

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About the article

Published Online: 2010-04-14

Published in Print: 2010-04-01


Citation Information: Open Mathematics, Volume 8, Issue 2, Pages 367–377, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-010-0009-4.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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