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Kannan-type cyclic contraction results in 2 -Menger space

Binayak S. Choudhury;  Samir Kumar BHANDARI — 2016

Mathematica Bohemica

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....

Cyclic Type Fixed Point Results in 2-Menger Spaces

Binayak S. Choudhury;  Samir Kumar BHANDARI;  Parbati SAHA — 2015

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we introduce generalized cyclic contractions through r number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t -norm. In another theorem we use a control function with minimum t -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.

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