Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications
In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/10/766 |
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| author | Fahad Jahangeer Salha Alshaikey Umar Ishtiaq Tania A. Lazăr Vasile L. Lazăr Liliana Guran |
| author_facet | Fahad Jahangeer Salha Alshaikey Umar Ishtiaq Tania A. Lazăr Vasile L. Lazăr Liliana Guran |
| author_sort | Fahad Jahangeer |
| collection | DOAJ |
| description | In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results. |
| first_indexed | 2024-03-10T21:14:05Z |
| format | Article |
| id | doaj.art-c9606a40701e4a6280fc2dea33c7393e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T21:14:05Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-c9606a40701e4a6280fc2dea33c7393e2023-11-19T16:35:00ZengMDPI AGFractal and Fractional2504-31102023-10-0171076610.3390/fractalfract7100766Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with ApplicationsFahad Jahangeer0Salha Alshaikey1Umar Ishtiaq2Tania A. Lazăr3Vasile L. Lazăr4Liliana Guran5Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, PakistanMathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 24381, Saudi ArabiaOffice of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaComputer Science Department, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaIn this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.https://www.mdpi.com/2504-3110/7/10/766bipolar metric spaceinterpolative proximal-type contractionsbest proximity pointsfixed pointsexistence and uniqueness |
| spellingShingle | Fahad Jahangeer Salha Alshaikey Umar Ishtiaq Tania A. Lazăr Vasile L. Lazăr Liliana Guran Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications Fractal and Fractional bipolar metric space interpolative proximal-type contractions best proximity points fixed points existence and uniqueness |
| title | Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications |
| title_full | Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications |
| title_fullStr | Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications |
| title_full_unstemmed | Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications |
| title_short | Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications |
| title_sort | certain interpolative proximal contractions best proximity point theorems in bipolar metric spaces with applications |
| topic | bipolar metric space interpolative proximal-type contractions best proximity points fixed points existence and uniqueness |
| url | https://www.mdpi.com/2504-3110/7/10/766 |
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