Some fixed-point theorems for mixed monotone operators in partially ordered probabilistic metric spaces

In this paper, some fixed-point theorems for nonlinear contractive operators in partially ordered Menger probabilistic metric spaces are proved. A new extension theorem of the probabilistic versions of Boyd and Wong’s nonlinear contraction theorem is presented. As a consequence, our main results improve and generalize some recent coupled fixed-point theorems and coincidence-point theorems in (Ćirić, Nonlinear Anal. 72:2009-2018, 2010; Jachymski, Nonlinear Anal., 73:2199-2203, 2010; Ćirić, Agarwal and Samet, Fixed Point Theory Appl. 2011:56, 2011).