A Kirk Type Characterization of Completeness for Partial Metric Spaces
We extend the celebrated result of W. A. Kirk that a metric space "Equation missing" is complete if and only if every Caristi self-mapping for "Equation missing" has a fixed point, to partial metric spaces.
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| Vydané v: | Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2010; číslo 1 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
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Cham
Springer International Publishing
01.01.2010
SpringerOpen |
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| ISSN: | 1687-1812, 1687-1820, 1687-1812 |
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| Abstract | We extend the celebrated result of W. A. Kirk that a metric space "Equation missing"
is complete if and only if every Caristi self-mapping for "Equation missing"
has a fixed point, to partial metric spaces. |
|---|---|
| AbstractList | We extend the celebrated result of W. A. Kirk that a metric space
is complete if and only if every Caristi self-mapping for
has a fixed point, to partial metric spaces. We extend the celebrated result of W. A. Kirk that a metric space X is complete if and only if every Caristi self-mapping for X has a fixed point, to partial metric spaces. We extend the celebrated result of W. A. Kirk that a metric space "Equation missing" is complete if and only if every Caristi self-mapping for "Equation missing" has a fixed point, to partial metric spaces. |
| ArticleNumber | 493298 |
| Author | Romaguera, Salvador |
| Author_xml | – sequence: 1 givenname: Salvador surname: Romaguera fullname: Romaguera, Salvador email: sromague@mat.upv.es organization: Insitituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia |
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| Cites_doi | 10.1023/A:1023012924892 10.1016/S0304-3975(02)00705-3 10.1006/jmaa.1998.6074 10.1090/S0002-9939-07-09055-7 10.2140/pjm.1977.69.339 10.1017/S0960129506005196 10.1007/BF01472580 10.1023/A:1008684018933 10.1016/j.na.2008.10.042 10.1016/j.jmaa.2004.08.019 10.1090/S0002-9947-1976-0394329-4 10.1016/j.topol.2005.01.023 10.1016/S1571-0661(04)00029-5 10.1017/S0960129509007671 10.1016/j.jmaa.2005.12.004 10.1007/BF02832367 10.4064/cm-36-1-81-86 10.12775/TMNA.1996.040 10.24033/msmf.266 10.4064/cm-49-1-21-26 |
| ContentType | Journal Article |
| Copyright | Salvador Romaguera. 2010. This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| References_xml | – volume: 11 start-page: 41 issue: 1 year: 2003 end-page: 67 ident: CR24 article-title: Quantitative continuous domains publication-title: Applied Categorical Structures doi: 10.1023/A:1023012924892 – volume: 305 start-page: 409 issue: 1–3 year: 2003 end-page: 432 ident: CR23 article-title: A characterization of partial metrizability: domains are quantifiable publication-title: Theoretical Computer Science doi: 10.1016/S0304-3975(02)00705-3 – volume: 227 start-page: 55 issue: 1 year: 1998 end-page: 67 ident: CR5 article-title: Caristi's fixed point theorem and selections of set-valued contractions publication-title: Journal of Mathematical Analysis and Applications doi: 10.1006/jmaa.1998.6074 – start-page: 7 year: 2009 ident: CR8 article-title: Generalized Caristi's fixed point theorems publication-title: Fixed Point Theory and Applications – volume: 136 start-page: 1861 issue: 5 year: 2008 end-page: 1869 ident: CR16 article-title: A generalized Banach contraction 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| Snippet | We extend the celebrated result of W. A. Kirk that a metric space
is complete if and only if every Caristi self-mapping for
has a fixed point, to partial... We extend the celebrated result of W. A. Kirk that a metric space "Equation missing" is complete if and only if every Caristi self-mapping for "Equation... We extend the celebrated result of W. A. Kirk that a metric space X is complete if and only if every Caristi self-mapping for X has a fixed point, to partial... |
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| SubjectTerms | Analysis Applications of Mathematics Differential Geometry Impact of Kirk's Results on the Development of Fixed Point Theory Mathematical and Computational Biology Mathematics Mathematics and Statistics Research Article Topology |
| Title | A Kirk Type Characterization of Completeness for Partial Metric Spaces |
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