Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces
Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spac...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/171624 |
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| _version_ | 1832549902174912512 |
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| author | Ravi P. Agarwal Hamed H. Alsulami Erdal Karapınar Farshid Khojasteh |
| author_facet | Ravi P. Agarwal Hamed H. Alsulami Erdal Karapınar Farshid Khojasteh |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces. |
| format | Article |
| id | doaj-art-f61887d4956a4c99bba2c4a74e6f8464 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f61887d4956a4c99bba2c4a74e6f84642025-02-03T06:08:24ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/171624171624Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric SpacesRavi P. Agarwal0Hamed H. Alsulami1Erdal Karapınar2Farshid Khojasteh3Department of Mathematics, Texas A&M University-Kingsville, MSC 172, Rhode Hall 217B, Kingsville, TX 78363-8202, USANonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi ArabiaNonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Mathematics, Islamic Azad University, Arak Branch, Arak, IranVery recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.http://dx.doi.org/10.1155/2014/171624 |
| spellingShingle | Ravi P. Agarwal Hamed H. Alsulami Erdal Karapınar Farshid Khojasteh Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces Abstract and Applied Analysis |
| title | Remarks on Some Recent Fixed Point Results on
Quaternion-Valued Metric Spaces |
| title_full | Remarks on Some Recent Fixed Point Results on
Quaternion-Valued Metric Spaces |
| title_fullStr | Remarks on Some Recent Fixed Point Results on
Quaternion-Valued Metric Spaces |
| title_full_unstemmed | Remarks on Some Recent Fixed Point Results on
Quaternion-Valued Metric Spaces |
| title_short | Remarks on Some Recent Fixed Point Results on
Quaternion-Valued Metric Spaces |
| title_sort | remarks on some recent fixed point results on quaternion valued metric spaces |
| url | http://dx.doi.org/10.1155/2014/171624 |
| work_keys_str_mv | AT ravipagarwal remarksonsomerecentfixedpointresultsonquaternionvaluedmetricspaces AT hamedhalsulami remarksonsomerecentfixedpointresultsonquaternionvaluedmetricspaces AT erdalkarapınar remarksonsomerecentfixedpointresultsonquaternionvaluedmetricspaces AT farshidkhojasteh remarksonsomerecentfixedpointresultsonquaternionvaluedmetricspaces |