Some Coupled Coincident Point Theorems in Metric Space

In this present work, we prove coupled coincident point theorem for contractive mappings F : X× X  X and g : X  X such that F  X  X   g  X  in metric spaces that have a nonempty F -invariant and g -invariant complete subset and we prove uniqueness coupled coincidence, then we prove coupled fixed point theorem for contractive mapping F in metric spaces that have a nonempty F -invariant complete subset. Finally, we give an example in this case. Through there are thousands of fixed point theorems in metric space, our theorems is a new type of theorems. because we prove unique coupled fixed point are in F -invariant complete subspace.