Best proximity points for alternative p-contractions
Abstract Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a suitable framework for the mirror reflection...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-024-03078-5 |
| _version_ | 1797349684051705856 |
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| author | Mi Zhou Nicolae Adrian Secelean Naeem Saleem Mujahid Abbas |
| author_facet | Mi Zhou Nicolae Adrian Secelean Naeem Saleem Mujahid Abbas |
| author_sort | Mi Zhou |
| collection | DOAJ |
| description | Abstract Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a suitable framework for the mirror reflection model. Alternative contraction mappings introduced by Chen (Symmetry 11:750, 2019) built a new model containing several mirrors in which the light reflected from a mirror does not go to the next mirror sequentially, and its path may diverge to any other mirror. The aim of this paper is to present a new variant of alternative contraction called alternative p-contraction and study its properties. The best proximity point result for such contractions under the alternative UC property is proved. An example to support the result proved herein is provided. |
| first_indexed | 2024-03-08T12:33:57Z |
| format | Article |
| id | doaj.art-e9b7e7bdd7a74fe587951773dbc145f1 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-08T12:33:57Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-e9b7e7bdd7a74fe587951773dbc145f12024-01-21T12:39:26ZengSpringerOpenJournal of Inequalities and Applications1029-242X2024-01-012024111710.1186/s13660-024-03078-5Best proximity points for alternative p-contractionsMi Zhou0Nicolae Adrian Secelean1Naeem Saleem2Mujahid Abbas3School of Science and Technology, University of SanyaDepartment of Mathematics and Computer Science, Faculty of Sciences, Lucian Blaga University of SibiuDepartment of Mathematics, University of Management and TechnologyDepartment of Mathematics, Government College UniversityAbstract Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a suitable framework for the mirror reflection model. Alternative contraction mappings introduced by Chen (Symmetry 11:750, 2019) built a new model containing several mirrors in which the light reflected from a mirror does not go to the next mirror sequentially, and its path may diverge to any other mirror. The aim of this paper is to present a new variant of alternative contraction called alternative p-contraction and study its properties. The best proximity point result for such contractions under the alternative UC property is proved. An example to support the result proved herein is provided.https://doi.org/10.1186/s13660-024-03078-5Best proximity pointAlternative UC propertyAlternative p-contraction |
| spellingShingle | Mi Zhou Nicolae Adrian Secelean Naeem Saleem Mujahid Abbas Best proximity points for alternative p-contractions Journal of Inequalities and Applications Best proximity point Alternative UC property Alternative p-contraction |
| title | Best proximity points for alternative p-contractions |
| title_full | Best proximity points for alternative p-contractions |
| title_fullStr | Best proximity points for alternative p-contractions |
| title_full_unstemmed | Best proximity points for alternative p-contractions |
| title_short | Best proximity points for alternative p-contractions |
| title_sort | best proximity points for alternative p contractions |
| topic | Best proximity point Alternative UC property Alternative p-contraction |
| url | https://doi.org/10.1186/s13660-024-03078-5 |
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