Two extensions of coupled coincidence point results for nonlinear contractive mappings

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 Ćirić (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 Ćirić (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.