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We establish some common coupled fixed point theorems for hybrid pair of mappings under generalized weak contraction on a non complete metric space, which is not partially ordered. As an application, we study the existence and uniqueness of the solution to an integral equation and also give an example to show the fruitfulness of our results. The results we obtain generalize, extend and improve several classical results in the literature in metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we prove some coupled fixed point theorems for Geraghty-type mappings having mixed monotone property and depending on another function in G-metric spaces. Moreover, we prove the uniqueness of the coupled fixed point. Our results generalize several comparable results in the literature. We also give some examples to prove the validity of our results. At the end, application to a certain class of non-linear integral equations is also obtained. [ABSTRACT FROM AUTHOR]