Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref>
The exploration of contractive inequalities which do not imply the continuity of the mapping at fixed points was an interesting open problem for quite some time. A significant amount of progress was made in the last two decades towards the solution of this problem. In the current paper, we attempt t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1605 |
| _version_ | 1797503842379628544 |
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| author | Pradip Debnath |
| author_facet | Pradip Debnath |
| author_sort | Pradip Debnath |
| collection | DOAJ |
| description | The exploration of contractive inequalities which do not imply the continuity of the mapping at fixed points was an interesting open problem for quite some time. A significant amount of progress was made in the last two decades towards the solution of this problem. In the current paper, we attempt to address the question of discontinuity at fixed point with the help of <i>F</i>-contractions in a metric space. We establish a common fixed-point (CFP) result for such contractive mappings and investigate its discontinuity at the CFP. A fixed-circle result is also obtained consequently. |
| first_indexed | 2024-03-10T03:56:08Z |
| format | Article |
| id | doaj.art-f6d806b66f114cd29b50e60fda7f1203 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:56:08Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f6d806b66f114cd29b50e60fda7f12032023-11-23T08:46:49ZengMDPI AGMathematics2227-73902022-05-01109160510.3390/math10091605Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref>Pradip Debnath0Department of Applied Science and Humanities, Assam University Silchar, Cachar 788011, Assam, IndiaThe exploration of contractive inequalities which do not imply the continuity of the mapping at fixed points was an interesting open problem for quite some time. A significant amount of progress was made in the last two decades towards the solution of this problem. In the current paper, we attempt to address the question of discontinuity at fixed point with the help of <i>F</i>-contractions in a metric space. We establish a common fixed-point (CFP) result for such contractive mappings and investigate its discontinuity at the CFP. A fixed-circle result is also obtained consequently.https://www.mdpi.com/2227-7390/10/9/1605discontinuityfixed pointcommon fixed pointF-contractioncomplete metric spacefixed-circle |
| spellingShingle | Pradip Debnath Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref> Mathematics discontinuity fixed point common fixed point F-contraction complete metric space fixed-circle |
| title | Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref> |
| title_full | Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref> |
| title_fullStr | Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref> |
| title_full_unstemmed | Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref> |
| title_short | Common Fixed-Point and Fixed-Circle Results for a Class of Discontinuous <i>F</i>-Contractive Mappings <xref rid="fn1-mathematics-1692711" ref-type="fn">†</xref> |
| title_sort | common fixed point and fixed circle results for a class of discontinuous i f i contractive mappings xref rid fn1 mathematics 1692711 ref type fn † xref |
| topic | discontinuity fixed point common fixed point F-contraction complete metric space fixed-circle |
| url | https://www.mdpi.com/2227-7390/10/9/1605 |
| work_keys_str_mv | AT pradipdebnath commonfixedpointandfixedcircleresultsforaclassofdiscontinuousificontractivemappingsxrefridfn1mathematics1692711reftypefnxref |