Fixed Point Theory and Fractals
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".
Deadline for manuscript submissions: 31 May 2025 | Viewed by 623
Special Issue Editors
Interests: fractals; fixed point theory; approximation; iterative methods
Special Issues, Collections and Topics in MDPI journals
Interests: fractal geometry; multifractal analysis; dynamical systems
2. CMAFcIO—Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, 1749-016 Lisbon, Portugal
Interests: fractals; fractal regression; Hausdorff dimension; fractal calculus; systems of iterative equations
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
In recent decades, fractal theory has proven to be extremely useful for the modelling of a great quantity of natural and social phenomena. Its fields of applications range from biotechnology to financial markets, for instance.
Fractal geometry builds a bridge between classical geometry and modern analysis. The static models of the old geometry are enriched with the dynamics of an infinite iterative process, where the outputs are not merely points but more sophisticated geometric objects and structures.
A fractal set can be described in very different ways, but the current mathematical research tends to define a fractal as the fixed point of an operator on the space of compact subsets of a space of metric type. Iterated function systems provide a way of constructing an operator of this kind, and a procedure for the approximation of its fixed points. Thus, the relationships between fractal and fixed-point theories are deep and increasingly intricate.
This issue is aimed at emphasizing the relationships between both fields, including their theoretical as well as their applied aspects. This volume also welcomes acute insights in any of the disciplines with potential (even if they are not developed) influences in the other.
Prof. Dr. María A. Navascués
Dr. Bilel Selmi
Dr. Cristina Serpa
Guest Editors
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Keywords
- fixed point theorems
- fractal sets, functions and measures
- fixed-point approximation and stability
- iterative methods for the solution of differential and integral equations
- iterated function systems
- discrete dynamical systems
- fractional calculus related to fixed point theory, dynamical systems or deterministic/stochastic fractals
- applications of these fields
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