Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application
This study aims to provide some new classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/1/243 |
| _version_ | 1797436765306355712 |
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| author | Khairul Habib Alam Yumnam Rohen Naeem Saleem |
| author_facet | Khairul Habib Alam Yumnam Rohen Naeem Saleem |
| author_sort | Khairul Habib Alam |
| collection | DOAJ |
| description | This study aims to provide some new classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><msup><mi>F</mi><mo>*</mo></msup><mo>)</mo></mrow></semantics></math></inline-formula>-weak Geraghty contraction and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><msup><mi>F</mi><mrow><mo>*</mo><mo>*</mo></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula>-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem. |
| first_indexed | 2024-03-09T11:07:20Z |
| format | Article |
| id | doaj.art-97ca3c53e4f740cda0f9641bd633a82a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T11:07:20Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-97ca3c53e4f740cda0f9641bd633a82a2023-12-01T00:54:01ZengMDPI AGSymmetry2073-89942023-01-0115124310.3390/sym15010243Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an ApplicationKhairul Habib Alam0Yumnam Rohen1Naeem Saleem2Department of Mathematics, National Institute of Techmology Manipur, Imphal 795004, IndiaDepartment of Mathematics, National Institute of Techmology Manipur, Imphal 795004, IndiaDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanThis study aims to provide some new classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><msup><mi>F</mi><mo>*</mo></msup><mo>)</mo></mrow></semantics></math></inline-formula>-weak Geraghty contraction and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><msup><mi>F</mi><mrow><mo>*</mo><mo>*</mo></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula>-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem.https://www.mdpi.com/2073-8994/15/1/243fixed point<i>F</i>-contraction<i>α</i>-admissible mapping(<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-weak Geraghty contractions |
| spellingShingle | Khairul Habib Alam Yumnam Rohen Naeem Saleem Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application Symmetry fixed point <i>F</i>-contraction <i>α</i>-admissible mapping (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-weak Geraghty contractions |
| title | Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application |
| title_full | Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application |
| title_fullStr | Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application |
| title_full_unstemmed | Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application |
| title_short | Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application |
| title_sort | fixed points of i α i i β i i f i and i α i i β i i f i weak geraghty contractions with an application |
| topic | fixed point <i>F</i>-contraction <i>α</i>-admissible mapping (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-weak Geraghty contractions |
| url | https://www.mdpi.com/2073-8994/15/1/243 |
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