Abstract
In this paper, we first review some important definitions and notions related to best proximity point theory by considering the lack of symmetry property of quasi metric. Then, we introduce a new notion of BG-multivalued contraction mappings. Then, a best proximity point result is obtained via Q-function on quasi metric. Also, we present a noteworthy illustrative example to show the effect of our results. Finally, we give an existence and uniqueness result for the solution of nonlinear integral equations via our result.
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