This article aims to prove some coupled fixed point (FP) theorems for nonlinear contractive type mapping in multiplicative metric space (MM-space). Our presented work consists of the maximum type and some other expressions in the framework of MM-space. We also provide illustrative examples and an application in support of our generalized results. Our offered results expand and develop a variety of the latest outcomes in the existing literature. Moreover, we present an application of the two Urysohn integral equations to support our work.