Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces”
In the recent paper “common fixed point theorems for commutating mappings in fuzzy metric spaces,” the authors proved that a common fixed point theorem for commutating mappings in G-complete fuzzy metric spaces and gave an example to illustrate the main result. In this note, we point out that the ab...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/142858 |
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| _version_ | 1832565496460869632 |
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| author | Yonghong Shen Wei Chen Sanfu Wang |
| author_facet | Yonghong Shen Wei Chen Sanfu Wang |
| author_sort | Yonghong Shen |
| collection | DOAJ |
| description | In the recent paper “common fixed point theorems for commutating mappings in fuzzy metric spaces,” the authors proved that a common fixed point theorem for commutating mappings in G-complete fuzzy metric spaces and gave an example to illustrate the main result. In this note, we point out that the above example is incorrect because it does not satisfy the condition of G-completeness, and then two appropriate examples are given. In addition, we prove that the theorem proposed by Zheng and Lian actually holds in an M-complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature. |
| format | Article |
| id | doaj-art-2f664771cf994c72986b6cd23959feff |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2f664771cf994c72986b6cd23959feff2025-02-03T01:07:27ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/142858142858Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces”Yonghong Shen0Wei Chen1Sanfu Wang2School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaSchool of Information, Capital University of Economics and Business, Beijing 100070, ChinaSchool of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, ChinaIn the recent paper “common fixed point theorems for commutating mappings in fuzzy metric spaces,” the authors proved that a common fixed point theorem for commutating mappings in G-complete fuzzy metric spaces and gave an example to illustrate the main result. In this note, we point out that the above example is incorrect because it does not satisfy the condition of G-completeness, and then two appropriate examples are given. In addition, we prove that the theorem proposed by Zheng and Lian actually holds in an M-complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature.http://dx.doi.org/10.1155/2012/142858 |
| spellingShingle | Yonghong Shen Wei Chen Sanfu Wang Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces” Abstract and Applied Analysis |
| title | Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces” |
| title_full | Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces” |
| title_fullStr | Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces” |
| title_full_unstemmed | Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces” |
| title_short | Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces” |
| title_sort | comment on common fixed point theorems for commutating mappings in fuzzy metric spaces |
| url | http://dx.doi.org/10.1155/2012/142858 |
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