Publication

Abstract : In this paper, we prove the existence and uniqueness of coupled fixed points for a mapping in an orthogonal set under a given contraction condition. Specifically, we first introduce the concept of orthogonal mixed property and orthogonal continuity type mappings on the product space of orthogonal sets. Using these concepts, we derive the coupled fixed point theorems. Furthermore, our results extend the coupled fixed point results in a partially ordered metric space obtained by Bhaskar and Lakshmikantham, as orthogonal sets are a more generalized class that is not comparable to partially ordered sets. Additionally, we provide an example where we can apply our results but not the results obtained by Bhaskar and Lakshmikantham. Our findings extend, improve, and generalize several known results in the literature.