Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points
The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/3/411 |
| _version_ | 1818008207075835904 |
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| author | Pradip Debnath Manuel de La Sen |
| author_facet | Pradip Debnath Manuel de La Sen |
| author_sort | Pradip Debnath |
| collection | DOAJ |
| description | The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities. |
| first_indexed | 2024-04-14T05:26:12Z |
| format | Article |
| id | doaj.art-41edd23577f44b71b95e6a32b4128c61 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T05:26:12Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-41edd23577f44b71b95e6a32b4128c612022-12-22T02:09:58ZengMDPI AGSymmetry2073-89942020-03-0112341110.3390/sym12030411sym12030411Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed PointsPradip Debnath0Manuel de La Sen1Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam 788011, IndiaInstitute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, 48940 Leioa (Bizakaia), SpainThe symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities.https://www.mdpi.com/2073-8994/12/3/411fixed pointasymptotically regular mapset-valued mapmetric spaceorbitally continuous map |
| spellingShingle | Pradip Debnath Manuel de La Sen Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points Symmetry fixed point asymptotically regular map set-valued map metric space orbitally continuous map |
| title | Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points |
| title_full | Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points |
| title_fullStr | Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points |
| title_full_unstemmed | Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points |
| title_short | Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points |
| title_sort | contractive inequalities for some asymptotically regular set valued mappings and their fixed points |
| topic | fixed point asymptotically regular map set-valued map metric space orbitally continuous map |
| url | https://www.mdpi.com/2073-8994/12/3/411 |
| work_keys_str_mv | AT pradipdebnath contractiveinequalitiesforsomeasymptoticallyregularsetvaluedmappingsandtheirfixedpoints AT manueldelasen contractiveinequalitiesforsomeasymptoticallyregularsetvaluedmappingsandtheirfixedpoints |