Solving Fredholm Integral Equations Using Probabilistic F-Contractions
Fixed-point theory plays a pivotal role in addressing equations that model various real-life applications, offering robust methods to find solutions that remain stable under different conditions and dynamics. The main objective of this paper is to introduce and study the novel concept of probabilist...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/2/119 |
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| Summary: | Fixed-point theory plays a pivotal role in addressing equations that model various real-life applications, offering robust methods to find solutions that remain stable under different conditions and dynamics. The main objective of this paper is to introduce and study the novel concept of probabilistic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-contraction within the framework of Menger spaces. This innovative approach extends classical fixed-point results to probabilistic settings, leveraging the probabilistic structure of Menger spaces to handle uncertainty and variability in the modeling process. By establishing the existence and uniqueness of fixed points in this versatile class of spaces, the study highlights the broader applicability and deeper significance of the probabilistic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-contraction. We explore the intricate interrelations among these fixed points, shedding light on their implications across different contexts and presenting insights into various theorem versions that enhance our understanding of their utility. Additionally, we propose a straightforward and effective approach for solving a system of Fredholm integral equations using fixed-point techniques specifically tailored for Menger spaces, illustrating their practical utility in tackling the complex mathematical models encountered in diverse fields. |
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| ISSN: | 2075-1680 |