Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces
Introducing the concept of ∑-semicompleteness in semimetric spaces, we extend Caristi’s fixed point theorem to ∑-semicomplete semimetric spaces. Via this extension, we characterize ∑-semicompleteness. We also give generalizations of the Banach contraction principle.
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/9435470 |
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| _version_ | 1849307758207172608 |
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| author | Tomonari Suzuki |
| author_facet | Tomonari Suzuki |
| author_sort | Tomonari Suzuki |
| collection | DOAJ |
| description | Introducing the concept of ∑-semicompleteness in semimetric spaces, we extend Caristi’s fixed point theorem to ∑-semicomplete semimetric spaces. Via this extension, we characterize ∑-semicompleteness. We also give generalizations of the Banach contraction principle. |
| format | Article |
| id | doaj-art-27f8c9a2ea4e4f75b375f2e3d1dfdf15 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-27f8c9a2ea4e4f75b375f2e3d1dfdf152025-08-20T03:54:38ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/94354709435470Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric SpacesTomonari Suzuki0Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, JapanIntroducing the concept of ∑-semicompleteness in semimetric spaces, we extend Caristi’s fixed point theorem to ∑-semicomplete semimetric spaces. Via this extension, we characterize ∑-semicompleteness. We also give generalizations of the Banach contraction principle.http://dx.doi.org/10.1155/2018/9435470 |
| spellingShingle | Tomonari Suzuki Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces Journal of Function Spaces |
| title | Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces |
| title_full | Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces |
| title_fullStr | Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces |
| title_full_unstemmed | Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces |
| title_short | Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces |
| title_sort | characterization of ∑ semicompleteness via caristi s fixed point theorem in semimetric spaces |
| url | http://dx.doi.org/10.1155/2018/9435470 |
| work_keys_str_mv | AT tomonarisuzuki characterizationofsemicompletenessviacaristisfixedpointtheoreminsemimetricspaces |