Fixed point and coupled fixed point theorems for generalized cyclic weak contractions in partially ordered probabilistic metric spaces

摘要

In this paper, we introduce the concept of new generalized cyclic weak contraction mappings and prove a class of fixed point theorems for such mappings in partially ordered probabilistic metric spaces. In addition, we also establish a coupled fixed point for mixed monotone mappings under contractive conditions in partially ordered probabilistic metric spaces. Our results extend and generalize Harjani et al. (Nonlinear anal. 71(2009)3403-3410) and Wu (Fixed Point Theory Appl. 2014(2014)49). Also, we introduce an example to support the validity of our results. Finally, an application of our results extends fixed point theorems for generalized weak contraction mappings in ordered metric spaces.