Volume 31, Issue 3
A Cyclic Probabilistic C-Contraction Results using Hadzic and Lukasiewicz T-Norms in Menger Spaces

Anal. Theory Appl., 31 (2015), pp. 283-298

Published online: 2017-07

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• Abstract

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

• Keywords

Menger space Cauchy sequence fixed point $\phi$-function $\psi$-function

54E40 54H25

TY - JOUR T1 - A Cyclic Probabilistic C-Contraction Results using Hadzic and Lukasiewicz T-Norms in Menger Spaces AU - B. S. Choudhury, S. K. Bhandari & P. Saha 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 KW - Cauchy sequence KW - fixed point KW - $\phi$-function KW - $\psi$-function AB - In this paper we introduce generalized cyclic C-contractionsthrough p number of subsets of a probabilistic metric space andestablish two fixed point results for such contractions. In ourfirst theorem we use the Hadzic type t-norm. In our next theoremwe use Lukasiewicz t-norm. Our results generalize the resultsof Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The resultsare illustrated with some examples.