A Cyclic Probabilistic $C$-Contraction Results Using Hadzic and Lukasiewicz $T$-Norms in Menger Spaces

Abstract

In this paper we introduce generalized cyclic $C$-contractions through $p$ number of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type $t$-norm. In our next theorem we use Lukasiewicz $t$-norm. Our results generalize the results of Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The results are illustrated with some examples.