Some new coupled fixed point theorems in partially ordered complete probabilistic metric spaces

In this paper, we weaken the notion of ψ of Luong and Thuan, [V. N. Luong, N. X. Thuan, Nonlinear Anal., 74 (2011), 983992] and prove some new coupled coincidences and coupled common fixed point theorems for mappings having a mixed gmonotone property in partially ordered complete probabilistic metric spaces. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.