Existence of Random Solutions for Weakly Contractive Random Integral Equations in Separable Banach Spaces
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Abstract
Introduction: This paper focuses on studying random integral equations in separable Banach spaces. Such equations often appear in mathematical models that involve uncertainty, random effects, or stochastic processes. We describe simple and general conditions that guarantee the existence of at least one measurable random solution. The analysis is based on basic properties of random operators and fixed point ideas that help to connect randomness with deterministic techniques. The presented method is flexible and can be applied to several types of random integral equations that occur in science, engineering, and applied mathematics. In addition, the paper provides a verified example that illustrates how the theoretical result can be applied to a specific case. This study aims to offer a clear and straightforward approach for researchers working with random equations and related mathematical models.
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References
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