Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning
Probabilistic functional equations have been used to analyze various models in computational biology and learning theory. It is worth noting that they are linked to the symmetry of a system of functional equations’ transformation. Our objective is to propose a generic probabilistic functional equati...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/8/1313 |
| _version_ | 1797522002246893568 |
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| author | Ali Turab Won-Gil Park Wajahat Ali |
| author_facet | Ali Turab Won-Gil Park Wajahat Ali |
| author_sort | Ali Turab |
| collection | DOAJ |
| description | Probabilistic functional equations have been used to analyze various models in computational biology and learning theory. It is worth noting that they are linked to the symmetry of a system of functional equations’ transformation. Our objective is to propose a generic probabilistic functional equation that can cover most of the mathematical models addressed in the existing literature. The notable fixed-point tools are utilized to examine the existence, uniqueness, and stability of the suggested equation’s solution. Two examples are also given to emphasize the significance of our findings. |
| first_indexed | 2024-03-10T08:20:25Z |
| format | Article |
| id | doaj.art-5afdd42e599243439bfa9daa9c895eb5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T08:20:25Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5afdd42e599243439bfa9daa9c895eb52023-11-22T09:59:14ZengMDPI AGSymmetry2073-89942021-07-01138131310.3390/sym13081313Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of LearningAli Turab0Won-Gil Park1Wajahat Ali2Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, ThailandDepartment of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, KoreaSchool of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaProbabilistic functional equations have been used to analyze various models in computational biology and learning theory. It is worth noting that they are linked to the symmetry of a system of functional equations’ transformation. Our objective is to propose a generic probabilistic functional equation that can cover most of the mathematical models addressed in the existing literature. The notable fixed-point tools are utilized to examine the existence, uniqueness, and stability of the suggested equation’s solution. Two examples are also given to emphasize the significance of our findings.https://www.mdpi.com/2073-8994/13/8/1313functional equationstabilityfixed points |
| spellingShingle | Ali Turab Won-Gil Park Wajahat Ali Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning Symmetry functional equation stability fixed points |
| title | Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning |
| title_full | Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning |
| title_fullStr | Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning |
| title_full_unstemmed | Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning |
| title_short | Existence, Uniqueness, and Stability Analysis of the Probabilistic Functional Equation Emerging in Mathematical Biology and the Theory of Learning |
| title_sort | existence uniqueness and stability analysis of the probabilistic functional equation emerging in mathematical biology and the theory of learning |
| topic | functional equation stability fixed points |
| url | https://www.mdpi.com/2073-8994/13/8/1313 |
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