Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions
The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mro...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-11-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/11/2206 |
| _version_ | 1797508363218583552 |
|---|---|
| author | Arshad Ali Khan Basit Ali |
| author_facet | Arshad Ali Khan Basit Ali |
| author_sort | Arshad Ali Khan |
| collection | DOAJ |
| description | The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>−</mo></mrow></semantics></math></inline-formula>metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>−</mo></mrow></semantics></math></inline-formula>metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature. |
| first_indexed | 2024-03-10T05:01:05Z |
| format | Article |
| id | doaj.art-4eadd1b7a56b489bab7cb5206491531a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:01:05Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4eadd1b7a56b489bab7cb5206491531a2023-11-23T01:46:58ZengMDPI AGSymmetry2073-89942021-11-011311220610.3390/sym13112206Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-ContractionsArshad Ali Khan0Basit Ali1Department of Mathematics, School of Science, University of Management and Technology, C-II, Johar Town, Lahore 54770, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, C-II, Johar Town, Lahore 54770, PakistanThe aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>−</mo></mrow></semantics></math></inline-formula>metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>−</mo></mrow></semantics></math></inline-formula>metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature.https://www.mdpi.com/2073-8994/13/11/2206completenessquasi-contractionbest proximity points<i>b</i>−metricnon-self mappings |
| spellingShingle | Arshad Ali Khan Basit Ali Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions Symmetry completeness quasi-contraction best proximity points <i>b</i>−metric non-self mappings |
| title | Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions |
| title_full | Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions |
| title_fullStr | Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions |
| title_full_unstemmed | Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions |
| title_short | Completeness of <i>b</i>−Metric Spaces and Best Proximity Points of Nonself Quasi-Contractions |
| title_sort | completeness of i b i metric spaces and best proximity points of nonself quasi contractions |
| topic | completeness quasi-contraction best proximity points <i>b</i>−metric non-self mappings |
| url | https://www.mdpi.com/2073-8994/13/11/2206 |
| work_keys_str_mv | AT arshadalikhan completenessofibimetricspacesandbestproximitypointsofnonselfquasicontractions AT basitali completenessofibimetricspacesandbestproximitypointsofnonselfquasicontractions |