| Title:
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Kannan-type cyclic contraction results in $2$-Menger space (English) |
| Author:
|
Choudhury, Binayak Samadder |
| Author:
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BHANDARI, Samir Kumar |
| Language:
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English |
| Journal:
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Mathematica Bohemica |
| ISSN:
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0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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141 |
| Issue:
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1 |
| Year:
|
2016 |
| Pages:
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37-58 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$2$-Menger space |
| Keyword:
|
Cauchy sequence |
| Keyword:
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fixed point |
| Keyword:
|
$\phi $-function |
| Keyword:
|
$\psi $-function |
| Keyword:
|
cyclic contraction |
| MSC:
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47H10 |
| MSC:
|
54E40 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 06562157 |
| idMR:
|
MR3475136 |
| DOI:
|
10.21136/MB.2016.3 |
| . |
| Date available:
|
2016-03-17T19:44:14Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144850 |
| . |
| Reference:
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