ON PROBABILISTIC (\epsilon,\lambda)-LOCAL CONTRACTION MAPPINGS AND A SYSTEM OF INTEGRAL EQUATIONS
Abstract
In this paper, we consider the concept of probabilistic $(\epsilon,\lambda)$-local contraction which is a generalization of probabilistic contraction of Sehgal type, and the concept of probabilistic G-metric space, which is a generalization of the Menger probabilistic metric space. Then we prove some new coupled fixed point theorems for uniformly locally contractive mappings on probabilistic metric spaces. Also, we establish some coupled fixed point theorems for contractive mappings in probabilistic G-metric space. The article includes some examples and an application to a system of integral equations which supports of main results.
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DOI: https://doi.org/10.22190/FUMI210314071L
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