Common coupled fixed point results in multiplicative metric spaces and applications

In the framework of a multiplicative metric space, by using the concept of w* compatible mappings, we establish some new common coupled fixed point theorems for two mappings satisfying \(\phi\)type contractive condition. We do not use the condition of continuity of any mapping for finding the coupled coincidence and common coupled fixed point. Meantime, we also provide some examples to support our new results. As an application, we provide an existence and uniqueness theorem of common solution for a class of nonlinear integral equations by using the obtained new result.