Ciric type $p$-cyclic contraction results for discontinues mappings

Binayak S. Choudhury, Samir Kumar Bhandari

Cyclic mappings constitute a recently introduced class of mappings which have appeared in a number of papers in the contexts of fixed point theory and in the theory of optimization. In this paper we consider $p$-cyclic contraction type mappings which are generalized cyclic contractions through $p$ number of subsets of a probabilistic metric space. Moreover the contractive mappings are discontinuous. We use Hadzic type $t$-norms in our theorems which is characterized by the equicontinuities of its iterates. We deduce two fixed point theorems. In one of the theorems we use a control function which is the counterpart of a function widely used in fixed point theory in metric spaces. The theorems are supported with examples. The work is in the line of research developing probabilistic fixed point theory.