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Kannan-type cyclic contraction results in 2 -Menger space

Binayak S. Choudhury; Samir Kumar BHANDARI

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 1, page 37-58
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Choudhury, Binayak S., and BHANDARI, Samir Kumar. "Kannan-type cyclic contraction results in $2$-Menger space." Mathematica Bohemica 141.1 (2016): 37-58. <http://eudml.org/doc/276821>.

@article{Choudhury2016,
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.},
author = {Choudhury, Binayak S., BHANDARI, Samir Kumar},
journal = {Mathematica Bohemica},
keywords = {$2$-Menger space; Cauchy sequence; fixed point; $\phi $-function; $\psi $-function; cyclic contraction},
language = {eng},
number = {1},
pages = {37-58},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Kannan-type cyclic contraction results in $2$-Menger space},
url = {http://eudml.org/doc/276821},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Choudhury, Binayak S.
AU - BHANDARI, Samir Kumar
TI - Kannan-type cyclic contraction results in $2$-Menger space
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 1
SP - 37
EP - 58
AB - 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.
LA - eng
KW - $2$-Menger space; Cauchy sequence; fixed point; $\phi $-function; $\psi $-function; cyclic contraction
UR - http://eudml.org/doc/276821
ER -

References

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