Geodesic
Kannan-type cyclic contraction results in $2$-Menger space
Mathematica Bohemica, Tome 141 (2016) no. 1, pp. 37-58.

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In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of $t$-norm in our theorems. In our first theorem we use a Hadzic-type $t$-norm. We use the minimum $t$-norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with an example.
DOI : 10.21136/MB.2016.3
Classification : 47H10, 54E40, 54H25
Keywords: $2$-Menger space; Cauchy sequence; fixed point; $\phi $-function; $\psi $-function; cyclic contraction 
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Choudhury, Binayak Samadder; BHANDARI, Samir Kumar. Kannan-type cyclic contraction results in $2$-Menger space. Mathematica Bohemica, Tome 141 (2016) no. 1, pp. 37-58. doi : 10.21136/MB.2016.3. http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.3/

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