In this paper, the notion of mixed f, g monotone mapping is introduced, and the coupled
coincidence point theorem for nonlinear contractive mappings in partially ordered complete metric
spaces has been proved. Presented theorems are generalizations of the recent fixed point theorems
due to Lakshmikantham and C´ iric´ (2009) [17] and include several recent developments. Also, using
the theory of countable extension of t-norm, it has been proved that a common fixed point theorem
given in C´ iric´ (2011) [12] hold for a more general classes of t-norms in fuzzy metric spaces. Their
theorem can be used to investigate a large class of problems and has discussed the existence and
uniqueness of solution for a periodic boundary value problem.