Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning
One-dimensional continuous functions are important fundament for studying other complex functions. Many theories and methods applied to study one-dimensional continuous functions can also be accustomed to investigating the properties of multi-dimensional functions. The properties of one-dimensional...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/2/69 |
| _version_ | 1797480119882743808 |
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| author | Wang Jun Cao Lei Wang Bin Gong Hongtao Tang Wei |
| author_facet | Wang Jun Cao Lei Wang Bin Gong Hongtao Tang Wei |
| author_sort | Wang Jun |
| collection | DOAJ |
| description | One-dimensional continuous functions are important fundament for studying other complex functions. Many theories and methods applied to study one-dimensional continuous functions can also be accustomed to investigating the properties of multi-dimensional functions. The properties of one-dimensional continuous functions, such as dimensionality, continuity, and boundedness, have been discussed from multiple perspectives. Therefore, the existing conclusions will be systematically sorted out according to the bounded variation, unbounded variation and h<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>o</mi><mo>¨</mo></mover></semantics></math></inline-formula>lder continuity. At the same time, unbounded variation points are used to analyze continuous functions and construct unbounded variation functions innovatively. Possible applications of fractal and fractal dimension in reinforcement learning are predicted. |
| first_indexed | 2024-03-09T21:56:03Z |
| format | Article |
| id | doaj.art-b82f7f2b63a5444b842c2e8026422b23 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:56:03Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-b82f7f2b63a5444b842c2e8026422b232023-11-23T19:58:41ZengMDPI AGFractal and Fractional2504-31102022-01-01626910.3390/fractalfract6020069Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement LearningWang Jun0Cao Lei1Wang Bin2Gong Hongtao3Tang Wei4College of Command Information System, Army Engineering University of PLA, Nanjing 210001, ChinaCollege of Command Information System, Army Engineering University of PLA, Nanjing 210001, ChinaTroops of 78092, Chengdu 610031, ChinaTroops of 78092, Chengdu 610031, ChinaCollege of Command Information System, Army Engineering University of PLA, Nanjing 210001, ChinaOne-dimensional continuous functions are important fundament for studying other complex functions. Many theories and methods applied to study one-dimensional continuous functions can also be accustomed to investigating the properties of multi-dimensional functions. The properties of one-dimensional continuous functions, such as dimensionality, continuity, and boundedness, have been discussed from multiple perspectives. Therefore, the existing conclusions will be systematically sorted out according to the bounded variation, unbounded variation and h<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>o</mi><mo>¨</mo></mover></semantics></math></inline-formula>lder continuity. At the same time, unbounded variation points are used to analyze continuous functions and construct unbounded variation functions innovatively. Possible applications of fractal and fractal dimension in reinforcement learning are predicted.https://www.mdpi.com/2504-3110/6/2/69continuous functionsunbounded variationfractal dimensionreinforcement learning |
| spellingShingle | Wang Jun Cao Lei Wang Bin Gong Hongtao Tang Wei Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning Fractal and Fractional continuous functions unbounded variation fractal dimension reinforcement learning |
| title | Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning |
| title_full | Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning |
| title_fullStr | Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning |
| title_full_unstemmed | Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning |
| title_short | Overview of One-Dimensional Continuous Functions with Fractional Integral and Applications in Reinforcement Learning |
| title_sort | overview of one dimensional continuous functions with fractional integral and applications in reinforcement learning |
| topic | continuous functions unbounded variation fractal dimension reinforcement learning |
| url | https://www.mdpi.com/2504-3110/6/2/69 |
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