On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph
We consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph. For that, we introduce the notions of nonself G-contraction and G-nonexpansive mappings, and we show that for each seminorm, we have a best proximity point. In addition, we conclude our wor...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/7481060 |
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| author | B. Saadaoui S. Lazaiz M. Aamri |
| author_facet | B. Saadaoui S. Lazaiz M. Aamri |
| author_sort | B. Saadaoui |
| collection | DOAJ |
| description | We consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph. For that, we introduce the notions of nonself G-contraction and G-nonexpansive mappings, and we show that for each seminorm, we have a best proximity point. In addition, we conclude our work with a result showing the existence of best proximity point for every seminorm. |
| format | Article |
| id | doaj-art-ed5a690e52e64a0ab1eabbbcdea73ba7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ed5a690e52e64a0ab1eabbbcdea73ba72025-02-03T01:06:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/74810607481060On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a GraphB. Saadaoui0S. Lazaiz1M. Aamri2Laboratory of Algebra, Analysis and Applications, Department of Mathematics, Ben M’sik Faculty of Sciences, University of Hassan II, Casablanca, MoroccoLASMA Laboratory, Department of Mathematics, Dhar El Mahraz Faculty of Sciences, University of Sidi Mohamed Ben Abdellah, Fes, MoroccoLaboratory of Algebra, Analysis and Applications, Department of Mathematics, Ben M’sik Faculty of Sciences, University of Hassan II, Casablanca, MoroccoWe consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph. For that, we introduce the notions of nonself G-contraction and G-nonexpansive mappings, and we show that for each seminorm, we have a best proximity point. In addition, we conclude our work with a result showing the existence of best proximity point for every seminorm.http://dx.doi.org/10.1155/2020/7481060 |
| spellingShingle | B. Saadaoui S. Lazaiz M. Aamri On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph International Journal of Mathematics and Mathematical Sciences |
| title | On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph |
| title_full | On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph |
| title_fullStr | On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph |
| title_full_unstemmed | On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph |
| title_short | On Best Proximity Point Theorems in Locally Convex Spaces Endowed with a Graph |
| title_sort | on best proximity point theorems in locally convex spaces endowed with a graph |
| url | http://dx.doi.org/10.1155/2020/7481060 |
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