Mathematica Bohemica, Vol. 141, No. 1, pp. 37-58, 2016
Kannan-type cyclic contraction results in $2$-Menger space
Binayak Samadder Choudhury, Samir Kumar Bhandari
Abstract: 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.
Affiliations: Binayak Samadder Choudhury, Department of Mathematics, Indian Institute of Engineering Science and Technology, Shipbur, P.O. Botanic Garden, Howrah, West Bengal 711103, India, e-mail: binayak12@yahoo.co.in; Samir Kumar Bhandari (corresponding author), Department of Mathematics, Bajkul Milani Mahavidyalaya, P.O. Kismat Bajkul, Bajkul, Purba Medinipur, West Bengal 721655, India, e-mail: skbhit@yahoo.co.in
