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

B. S. Choudhury, S. K. Bhandari & P. Saha

DOI: 10.4208/ata.2015.v31.n3.6

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

Published online: 2017-07

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  • Abstract

In this paper we introduce generalized cyclic $C$-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.

  • Keywords

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

  • AMS Subject Headings

54E40, 54H25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-31-283, author = {}, title = {A Cyclic Probabilistic $C$-Contraction Results Using Hadzic and Lukasiewicz $T$-Norms in Menger Spaces}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {3}, pages = {283--298}, 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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n3.6}, url = {http://global-sci.org/intro/article_detail/ata/4640.html} }
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 -

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.

B. S. Choudhury, S. K. Bhandari & P. Saha. (1970). A Cyclic Probabilistic $C$-Contraction Results Using Hadzic and Lukasiewicz $T$-Norms in Menger Spaces. Analysis in Theory and Applications. 31 (3). 283-298. doi:10.4208/ata.2015.v31.n3.6
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