Fixed Point and Tripled Fixed Point Theorems under Pata-Type Conditions in Ordered Metric Spaces
In this paper, we first prove a version of the fixed point theorem obtained in [V. Pata, A fixed point theorem in metric spaces, J. Fixed Point Theory Appl. 10 (2011) 299–305], adjusted for monotone mappings in ordered metric spaces, as well as some generalizations. Then we apply them to obtain results of this type for tripled fixed points in two cases—for monotone and mixed-monotone mappings with three variables. An example is given to show the difference between some of these results.