Binayak S. Choudhury, Samir Kumar Bhandari, Parbati Saha
February 13, 2018
Cyclic mappings have appeared prominently in fixed point theory during the last decade. They have also their applications in global optimization problems. Note that p -cyclic mappings are extensions of cyclic mappings over p number of sets. In this paper we introduce two p -cyclic contractions in probabilistic spaces. We have two corresponding fixed point theorems using third-order Hadzic-type t -norm and minimum t -norm, respectively. One of the probabilistic contractions is of Ciric type while the other is a general contraction. One illustrative example is given. The space we consider here is a 2-Menger space which is an extension of a probabilistic metric space in the same vein as the 2-metric spaces are extensions of metric spaces.