Best Proximity Point Theorem in Quasi-Pseudometric Spaces
In quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/9784592 |
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| _version_ | 1832562739951697920 |
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| author | Robert Plebaniak |
| author_facet | Robert Plebaniak |
| author_sort | Robert Plebaniak |
| collection | DOAJ |
| description | In quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we proved new best proximity point theorem in a quasi-pseudometric space. A best proximity point theorem furnishes sufficient conditions that ascertain the existence of an optimal solution to the problem of globally minimizing the error inf{d(x,y):y∈T(x)}, and hence the existence of a consummate approximate solution to the equation T(X)=x. |
| format | Article |
| id | doaj-art-675c719c71114e8384791fc8f2e69aae |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-675c719c71114e8384791fc8f2e69aae2025-02-03T01:21:58ZengWileyAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/97845929784592Best Proximity Point Theorem in Quasi-Pseudometric SpacesRobert Plebaniak0Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, PolandIn quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we proved new best proximity point theorem in a quasi-pseudometric space. A best proximity point theorem furnishes sufficient conditions that ascertain the existence of an optimal solution to the problem of globally minimizing the error inf{d(x,y):y∈T(x)}, and hence the existence of a consummate approximate solution to the equation T(X)=x.http://dx.doi.org/10.1155/2016/9784592 |
| spellingShingle | Robert Plebaniak Best Proximity Point Theorem in Quasi-Pseudometric Spaces Abstract and Applied Analysis |
| title | Best Proximity Point Theorem in Quasi-Pseudometric Spaces |
| title_full | Best Proximity Point Theorem in Quasi-Pseudometric Spaces |
| title_fullStr | Best Proximity Point Theorem in Quasi-Pseudometric Spaces |
| title_full_unstemmed | Best Proximity Point Theorem in Quasi-Pseudometric Spaces |
| title_short | Best Proximity Point Theorem in Quasi-Pseudometric Spaces |
| title_sort | best proximity point theorem in quasi pseudometric spaces |
| url | http://dx.doi.org/10.1155/2016/9784592 |
| work_keys_str_mv | AT robertplebaniak bestproximitypointtheoreminquasipseudometricspaces |