Fixed Point Theory and Fractals
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 application range from biotechnology to financial markets, for instance. Fractal geometry builds a bridge between classical geometry and modern ana...
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| Format: | Online |
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| Langue: | anglais |
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MDPI - Multidisciplinary Digital Publishing Institute
2026
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| Accès en ligne: | ONIX_20260416T142754_9783725854035_4 |
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| _version_ | 1869515082760716288 |
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| collection | Directory of Open Access Books |
| description | 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 application 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 a 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 Reprint is aimed at emphasizing the relationships between both fields, including their theoretical and their applied aspects. |
| format | Online |
| id | doab-20.500.12854ir-174749 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1747492026-04-16T16:13:21Z Fixed Point Theory and Fractals Navascués, María Selmi, Bilel Serpa, Cristina Fixed Point Theory Fractals Contractions Fractal Functions Fractional Differential Equations Integral Equations Fuzzy Metric Spaces thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science 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 application 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 a 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 Reprint is aimed at emphasizing the relationships between both fields, including their theoretical and their applied aspects. 2026-04-16T16:13:12Z 2026-04-16T16:13:12Z 2025 book ONIX_20260416T142754_9783725854035_4 9783725854035 9783725854042 https://directory.doabooks.org/handle/20.500.12854/174749 eng application/octet-stream Attribution 4.0 International https://mdpi.com/books/ https://mdpi.com/books/pdfview/book/11627 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-7258-5404-2 10.3390/books978-3-7258-5404-2 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783725854035 9783725854042 194 CH open access |
| spellingShingle | Fixed Point Theory Fractals Contractions Fractal Functions Fractional Differential Equations Integral Equations Fuzzy Metric Spaces thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Fixed Point Theory and Fractals |
| title | Fixed Point Theory and Fractals |
| title_full | Fixed Point Theory and Fractals |
| title_fullStr | Fixed Point Theory and Fractals |
| title_full_unstemmed | Fixed Point Theory and Fractals |
| title_short | Fixed Point Theory and Fractals |
| title_sort | fixed point theory and fractals |
| topic | Fixed Point Theory Fractals Contractions Fractal Functions Fractional Differential Equations Integral Equations Fuzzy Metric Spaces thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | Fixed Point Theory Fractals Contractions Fractal Functions Fractional Differential Equations Integral Equations Fuzzy Metric Spaces thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20260416T142754_9783725854035_4 |