Probabilistic p-cyclic contractions using different types of t-norms

Abstract

Abstract 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.