TY - JOUR
T1 - A Cyclic Probabilistic $C$-Contraction Results Using Hadzic and Lukasiewicz $T$-Norms in Menger Spaces
JO - Analysis in Theory and Applications
VL - 3
SP - 283
EP - 298
PY - 2017
DA - 2017/07
SN - 31
DO - http://doi.org/10.4208/ata.2015.v31.n3.6
UR - https://global-sci.org/intro/article_detail/ata/4640.html
KW - Menger space, Cauchy sequence, fixed point, $\phi$-function, $\psi$-function,
AB - <p style="text-align: justify;">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.</p>